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Journal articles on the topic 'RCD spaces'

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Published: 11 March 2023

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1

Honda, Shouhei. "Isometric immersions of RCD spaces." Commentarii Mathematici Helvetici 96, no. 3 (November 22, 2021): 515–59. http://dx.doi.org/10.4171/cmh/519.

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2

Han, Bang-Xian. "Ricci Tensor on $$\mathrm{RCD}^*(K, N)$$ RCD ∗ ( K , N ) Spaces." Journal of Geometric Analysis 28, no. 2 (May 13, 2017): 1295–314. http://dx.doi.org/10.1007/s12220-017-9863-7.

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3

Mondino, Andrea, and Guofang Wei. "On the universal cover and the fundamental group of an RCD*(K,N)-space." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 753 (August 1, 2019): 211–37. http://dx.doi.org/10.1515/crelle-2016-0068.

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AbstractThe main goal of the paper is to prove the existence of the universal cover for {\mathsf{RCD}^{*}(K,N)}-spaces. This generalizes earlier work of [43, 44] on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental group of {\mathsf{RCD}^{*}(K,N)}-spaces. These are the first topological results for {\mathsf{RCD}^{*}(K,N)}-spaces without extra structural-topological assumptions (such as semi-local simple connectedness).
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4

Kitabeppu, Yu, and Sajjad Lakzian. "Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups." Canadian Mathematical Bulletin 58, no. 4 (December 1, 2015): 787–98. http://dx.doi.org/10.4153/cmb-2015-052-4.

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AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.
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5

Kuwada, Kazumasa, and Kazuhrio Kuwae. "Radial processes on RCD⁎(K,N) spaces." Journal de Mathématiques Pures et Appliquées 126 (June 2019): 72–108. http://dx.doi.org/10.1016/j.matpur.2018.12.008.

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6

Honda, Shouhei. "New differential operator and noncollapsed RCD spaces." Geometry & Topology 24, no. 4 (November 10, 2020): 2127–48. http://dx.doi.org/10.2140/gt.2020.24.2127.

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7

Debin, Clément, Nicola Gigli, and Enrico Pasqualetto. "Quasi-Continuous Vector Fields on RCD Spaces." Potential Analysis 54, no. 1 (February 18, 2020): 183–211. http://dx.doi.org/10.1007/s11118-019-09823-6.

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8

Huang, Xian-Tao. "Non-compact $$\text {RCD}(0,N)$$ RCD ( 0 , N ) Spaces with Linear Volume Growth." Journal of Geometric Analysis 28, no. 2 (May 4, 2017): 1005–51. http://dx.doi.org/10.1007/s12220-017-9852-x.

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9

Kapovitch, Vitali, and Christian Ketterer. "Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds." Analysis and Geometry in Metric Spaces 7, no. 1 (January 1, 2019): 197–211. http://dx.doi.org/10.1515/agms-2019-0010.

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10

Han, Bang-Xian. "Rigidity of some functional inequalities on RCD spaces." Journal de Mathématiques Pures et Appliquées 145 (January 2021): 163–203. http://dx.doi.org/10.1016/j.matpur.2020.07.004.

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11

Ambrosio, Luigi, and Shouhei Honda. "Local spectral convergence in RCD∗(K,N) spaces." Nonlinear Analysis 177 (December 2018): 1–23. http://dx.doi.org/10.1016/j.na.2017.04.003.

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12

Gigli, Nicola, and Luca Tamanini. "Second order differentiation formula on RCD*$(K,N)$ spaces." Journal of the European Mathematical Society 23, no. 5 (February 2, 2021): 1727–95. http://dx.doi.org/10.4171/jems/1042.

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13

Gigli, Nicola. "Lecture Notes On Differential Calculus on $\mathscr {RCD}$ Spaces." Publications of the Research Institute for Mathematical Sciences 54, no. 4 (October 18, 2018): 855–918. http://dx.doi.org/10.4171/prims/54-4-4.

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14

Gigli, Nicola, Christian Ketterer, Kazumasa Kuwada, and Shin-Ichi Ohta. "Rigidity for the spectral gap on Rcd(K, ∞)-spaces." American Journal of Mathematics 142, no. 5 (2020): 1559–94. http://dx.doi.org/10.1353/ajm.2020.0039.

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15

Brué, Elia, and Daniele Semola. "Regularity of Lagrangian flows over RCD*(K, N) spaces." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (August 1, 2020): 171–203. http://dx.doi.org/10.1515/crelle-2019-0027.

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AbstractThe aim of this note is to provide regularity results for Regular Lagrangian flows of Sobolev vector fields over compact metric measure spaces verifying the Riemannian curvature dimension condition. We first prove, borrowing some ideas already present in the literature, that flows generated by vector fields with bounded symmetric derivative are Lipschitz, providing the natural extension of the standard Cauchy–Lipschitz theorem to this setting. Then we prove a Lusin-type regularity result in the Sobolev case (under the additional assumption that the m.m.s. is Ahlfors regular) therefore extending the already known Euclidean result.
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16

Gigli, Nicola, and Luca Tamanini. "Second order differentiation formula on RCD$(K,N)$ spaces." Rendiconti Lincei - Matematica e Applicazioni 29, no. 2 (April 26, 2018): 377–86. http://dx.doi.org/10.4171/rlm/811.

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17

Gigli, Nicola, and Enrico Pasqualetto. "On the notion of parallel transport on RCD spaces." Revista Matemática Iberoamericana 36, no. 2 (December 17, 2019): 571–609. http://dx.doi.org/10.4171/rmi/1140.

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18

Gigli, Nicola. "Riemann curvature tensor on RCD spaces and possible applications." Comptes Rendus Mathematique 357, no. 7 (July 2019): 613–19. http://dx.doi.org/10.1016/j.crma.2019.06.003.

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19

Gigli, Nicola, and Chiara Rigoni. "A Note About the Strong Maximum Principle on RCD Spaces." Canadian Mathematical Bulletin 62, no. 02 (January 7, 2019): 259–66. http://dx.doi.org/10.4153/cmb-2018-022-9.

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20

Sturm, Karl-Theodor. "Distribution-Valued Ricci Bounds for Metric Measure Spaces, Singular Time Changes, and Gradient Estimates for Neumann Heat Flows." Geometric and Functional Analysis 30, no. 6 (November 20, 2020): 1648–711. http://dx.doi.org/10.1007/s00039-020-00554-0.

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AbstractWe will study metric measure spaces $$(X,\mathsf{d},{\mathfrak {m}})$$ ( X , d , m ) beyond the scope of spaces with synthetic lower Ricci bounds. In particular, we introduce distribution-valued lower Ricci bounds $$\mathsf{BE}_1(\kappa ,\infty )$$ BE 1 ( κ , ∞ ) for which we prove the equivalence with sharp gradient estimates, the class of which will be preserved under time changes with arbitrary $$\psi \in \mathrm {Lip}_b(X)$$ ψ ∈ Lip b ( X ) , and which are satisfied for the Neumann Laplacian on arbitrary semi-convex subsets $$Y\subset X$$ Y ⊂ X . In the latter case, the distribution-valued Ricci bound will be given by the signed measure $$\kappa = k\,{\mathfrak {m}}_Y + \ell \,\sigma _{\partial Y}$$ κ = k m Y + ℓ σ ∂ Y where k denotes a variable synthetic lower bound for the Ricci curvature of X and $$\ell $$ ℓ denotes a lower bound for the “curvature of the boundary” of Y, defined in purely metric terms. We also present a new localization argument which allows us to pass on the RCD property to arbitrary open subsets of RCD spaces. And we introduce new synthetic notions for boundary curvature, second fundamental form, and boundary measure for subsets of RCD spaces.
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21

Honda, Shouhei. "Bakry-Émery Conditions on Almost Smooth Metric Measure Spaces." Analysis and Geometry in Metric Spaces 6, no. 1 (October 1, 2018): 129–45. http://dx.doi.org/10.1515/agms-2018-0007.

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Abstract In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K, N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells us that the BE condition is strictly weaker than the RCD condition even in this setting, and that the local dimension is not constant even if the space satisfies the BE condition with the coincidence between the induced distance by the Cheeger energy and the original distance. In particular, the glued space gives a first example with a Ricci bound from below in the Bakry-Émery sense, whose local dimension is not constant. We also give a necessary and sufficient condition for such spaces to be RCD(K, N) spaces.
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22

Ambrosio, Luigi, Shouhei Honda, Jacobus W. Portegies, and David Tewodrose. "Embedding of RCD⁎(K,N) spaces in L2 via eigenfunctions." Journal of Functional Analysis 280, no. 10 (May 2021): 108968. http://dx.doi.org/10.1016/j.jfa.2021.108968.

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23

Han, Bang-Xian. "New characterizations of Ricci curvature on RCD metric measure spaces." Discrete & Continuous Dynamical Systems - A 38, no. 10 (2018): 4915–27. http://dx.doi.org/10.3934/dcds.2018214.

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24

Bruè, Elia, Enrico Pasqualetto, and Daniele Semola. "Rectifiability of RCD(K,N) spaces via δ-splitting maps." Annales Fennici Mathematici 46, no. 1 (June 2021): 465–82. http://dx.doi.org/10.5186/aasfm.2021.4627.

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25

Li, Huaiqian. "Dimension-Free Harnack Inequalities on $$\hbox {RCD}(K, \infty )$$ Spaces." Journal of Theoretical Probability 29, no. 4 (May 29, 2015): 1280–97. http://dx.doi.org/10.1007/s10959-015-0621-0.

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26

Gigli, Nicola, and Bang-Xian Han. "Independence on p of weak upper gradients on RCD spaces." Journal of Functional Analysis 271, no. 1 (July 2016): 1–11. http://dx.doi.org/10.1016/j.jfa.2016.04.014.

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27

Zhang, Hui-Chun, and Xi-Ping Zhu. "Weyl’s law on $RCD^{\ast} (K, N)$ metric measure spaces." Communications in Analysis and Geometry 27, no. 8 (2019): 1869–914. http://dx.doi.org/10.4310/cag.2019.v27.n8.a8.

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28

Li, Huaiqian. "Weighted Littlewood–Paley inequalities for heat flows in RCD spaces." Journal of Mathematical Analysis and Applications 479, no. 2 (November 2019): 1618–40. http://dx.doi.org/10.1016/j.jmaa.2019.07.015.

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29

Gigli, Nicola, and Luca Tamanini. "Benamou–Brenier and duality formulas for the entropic cost on $${\textsf {RCD}}^*(K,N)$$RCD∗(K,N) spaces." Probability Theory and Related Fields 176, no. 1-2 (April 30, 2019): 1–34. http://dx.doi.org/10.1007/s00440-019-00909-1.

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30

Kemper, Matthias, and Joachim Lohkamp. "Potential Theory on Gromov Hyperbolic Spaces." Analysis and Geometry in Metric Spaces 10, no. 1 (January 1, 2022): 394–431. http://dx.doi.org/10.1515/agms-2022-0147.

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Abstract Gromov hyperbolic spaces have become an essential concept in geometry, topology and group theory. Herewe extend Ancona’s potential theory on Gromov hyperbolic manifolds and graphs of bounded geometry to a large class of Schrödinger operators on Gromov hyperbolic metric measure spaces, unifying these settings in a common framework ready for applications to singular spaces such as RCD spaces or minimal hypersurfaces. Results include boundary Harnack inequalities and a complete classification of positive harmonic functions in terms of the Martin boundary which is identified with the geometric Gromov boundary.
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31

Ambrosio, Luigi, Shouhei Honda, and David Tewodrose. "Short-time behavior of the heat kernel and Weyl’s law on $${{\mathrm{RCD}}}^*(K,N)$$ RCD ∗ ( K , N ) spaces." Annals of Global Analysis and Geometry 53, no. 1 (August 15, 2017): 97–119. http://dx.doi.org/10.1007/s10455-017-9569-x.

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32

De Ponti, Nicolò, Andrea Mondino, and Daniele Semola. "The equality case in Cheeger's and Buser's inequalities on RCD spaces." Journal of Functional Analysis 281, no. 3 (August 2021): 109022. http://dx.doi.org/10.1016/j.jfa.2021.109022.

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33

Brué, Elia, Qin Deng, and Daniele Semola. "Improved regularity estimates for Lagrangian flows on RCD(K,N) spaces." Nonlinear Analysis 214 (January 2022): 112609. http://dx.doi.org/10.1016/j.na.2021.112609.

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34

Gigli, Nicola, and Enrico Pasqualetto. "Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts." Communications in Analysis and Geometry 29, no. 6 (2021): 1391–414. http://dx.doi.org/10.4310/cag.2021.v29.n6.a3.

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35

Han, Bang-Xian, and Andrea Mondino. "Angles between Curves in Metric Measure Spaces." Analysis and Geometry in Metric Spaces 5, no. 1 (September 2, 2017): 47–68. http://dx.doi.org/10.1515/agms-2017-0003.

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Abstract The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N) metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.
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36

Antonelli, Gioacchino, Elia Brué, and Daniele Semola. "Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces." Analysis and Geometry in Metric Spaces 7, no. 1 (January 1, 2019): 158–78. http://dx.doi.org/10.1515/agms-2019-0008.

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Abstract The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13]. The proof, which is based on a quantitative differentiation argument, closely follows the original one. As a simple outcome we provide a volume estimate for the enlargement of Gigli-DePhilippis’ boundary ([20, Remark 3.8]) of ncRCD(K, N) spaces.
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37

Huang, Jia-Cheng, and Hui-Chun Zhang. "Localized elliptic gradient estimate for solutions of the heat equation on $${ RCD}^*(K,N)$$RCD∗(K,N) metric measure spaces." manuscripta mathematica 161, no. 3-4 (December 6, 2018): 303–24. http://dx.doi.org/10.1007/s00229-018-1095-z.

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38

Kapovitch, Vitali, and Andrea Mondino. "On the topology and the boundary of N–dimensional RCD(K,N) spaces." Geometry & Topology 25, no. 1 (March 2, 2021): 445–95. http://dx.doi.org/10.2140/gt.2021.25.445.

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39

Ambrosio, Luigi, and Andrea Mondino. "Gaussian-type isoperimetric inequalities in RCD $(K, \infty)$ probability spaces for positive $K$." Rendiconti Lincei - Matematica e Applicazioni 27, no. 4 (2016): 497–514. http://dx.doi.org/10.4171/rlm/745.

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40

Huang, Jia-Cheng. "Local gradient estimates for heat equation on $RCD^*(k,n)$ metric measure spaces." Proceedings of the American Mathematical Society 146, no. 12 (September 4, 2018): 5391–407. http://dx.doi.org/10.1090/proc/14185.

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41

Huang, Jia-Cheng. "Li-Yau Inequality for Heat Equations on RCD∗(K,N) Metric Measure Spaces." Potential Analysis 53, no. 1 (February 9, 2019): 315–28. http://dx.doi.org/10.1007/s11118-019-09770-2.

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42

Ambrosio, Luigi, Elia Bruè, and Dario Trevisan. "Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and RCD(K,∞) spaces." Advances in Mathematics 339 (December 2018): 426–52. http://dx.doi.org/10.1016/j.aim.2018.09.033.

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43

Guijarro, Luis, and Jaime Santos-Rodríguez. "On the isometry group of $$RCD^*(K,N)$$ R C D ∗ ( K , N ) -spaces." manuscripta mathematica 158, no. 3-4 (March 5, 2018): 441–61. http://dx.doi.org/10.1007/s00229-018-1010-7.

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44

Brué, Elia, and Daniele Semola. "Constancy of the Dimension for RCD( K , N ) Spaces via Regularity of Lagrangian Flows." Communications on Pure and Applied Mathematics 73, no. 6 (June 2020): 1141–204. http://dx.doi.org/10.1002/cpa.21849.

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45

Huang, Xian-Tao. "An almost rigidity theorem and its applications to noncompact RCD(0,N) spaces with linear volume growth." Communications in Contemporary Mathematics 22, no. 04 (December 13, 2018): 1850076. http://dx.doi.org/10.1142/s0219199718500761.

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The main results of this paper consist of two parts. First, we obtain an almost rigidity theorem which roughly says that on an [Formula: see text] space, when a domain between two level sets of a distance function has almost maximal volume compared to that of a cylinder, then this portion is close to a cylinder as a metric space. Second, we apply this almost rigidity theorem to study noncompact [Formula: see text] spaces with linear volume growth. More precisely, we obtain the sublinear growth of diameter of geodesic spheres, and study the non-existence problem of nonconstant harmonic functions with polynomial growth on such [Formula: see text] spaces.
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46

Ambrosio, Luigi, Andrea Mondino, and Giuseppe Savaré. "On the Bakry–Émery Condition, the Gradient Estimates and the Local-to-Global Property of $$\mathsf{RCD}^*(K,N)$$ RCD ∗ ( K , N ) Metric Measure Spaces." Journal of Geometric Analysis 26, no. 1 (October 7, 2014): 24–56. http://dx.doi.org/10.1007/s12220-014-9537-7.

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47

Ambrosio, Luigi, Elia Brué, and Daniele Semola. "Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces." Geometric and Functional Analysis 29, no. 4 (July 1, 2019): 949–1001. http://dx.doi.org/10.1007/s00039-019-00504-5.

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48

Kitabeppu, Yu. "A finite diameter theorem on $${ RCD }(K,\infty )$$ R C D ( K , ∞ ) spaces for positive K." Mathematische Zeitschrift 283, no. 3-4 (February 9, 2016): 895–907. http://dx.doi.org/10.1007/s00209-016-1626-9.

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49

Nguyen, Hoang T. "The effects of plant spacing and frequency of aeration on the growth and yield of water dropwort (Oenanthe javanica (Blume) DC.) in hydroponic system." Journal of Agriculture and Development 17, no. 04 (August 28, 2018): 28–34. http://dx.doi.org/10.52997/jad.4.04.2018.

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Water dropwort is an aquatic perennial plant of the Apiaceae family and is a wild vegetable originating in the tropics of Asia. The plant prefers moist soil and growing in partial shading 60 - 70% conditions. The two factor experiments were arranged in randomized complete design (RCD) with three replications. Factor A was four planting spaces (4 × 2 cm; 4 × 3 cm; 4 × 4 cm and 4 × 5 cm). Factor B was frequency of aeration (every two days; every four days and every six days). Results showed that water dropwort planted in watercress nutritious solution at different planting spaces and frequency of aeration had no statistically significant effect on height, number of leaves/plant, average plant weight as well as quality indicators. However, water dropwort planted in watercress nutritious solution with 4 × 2 cm spacing and aerating for highest theoretical yield, actual yield and commercial yield are 3,408 kg/1,000 m2; 2,504 kg/1,000 m2 and 1,979 kg/1,000 m2.
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50

Savaré, Giuseppe. "Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in $RCD (K, \infty)$ metric measure spaces." Discrete & Continuous Dynamical Systems - A 34, no. 4 (2014): 1641–61. http://dx.doi.org/10.3934/dcds.2014.34.1641.

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