Articles de revues : « RCD spaces »

1

Honda, Shouhei. « Isometric immersions of RCD spaces ». Commentarii Mathematici Helvetici 96, n^o 3 (22 novembre 2021) : 515–59. http://dx.doi.org/10.4171/cmh/519.

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Han, Bang-Xian. « Ricci Tensor on $$\mathrm{RCD}^*(K, N)$$ RCD ∗ ( K , N ) Spaces ». Journal of Geometric Analysis 28, n^o 2 (13 mai 2017) : 1295–314. http://dx.doi.org/10.1007/s12220-017-9863-7.

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Mondino, Andrea, et 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, n^o 753 (1 août 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, et Sajjad Lakzian. « Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups ». Canadian Mathematical Bulletin 58, n^o 4 (1 décembre 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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Kuwada, Kazumasa, et Kazuhrio Kuwae. « Radial processes on RCD⁎(K,N) spaces ». Journal de Mathématiques Pures et Appliquées 126 (juin 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, n^o 4 (10 novembre 2020) : 2127–48. http://dx.doi.org/10.2140/gt.2020.24.2127.

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Debin, Clément, Nicola Gigli et Enrico Pasqualetto. « Quasi-Continuous Vector Fields on RCD Spaces ». Potential Analysis 54, n^o 1 (18 février 2020) : 183–211. http://dx.doi.org/10.1007/s11118-019-09823-6.

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Huang, Xian-Tao. « Non-compact $$\text {RCD}(0,N)$$ RCD ( 0 , N ) Spaces with Linear Volume Growth ». Journal of Geometric Analysis 28, n^o 2 (4 mai 2017) : 1005–51. http://dx.doi.org/10.1007/s12220-017-9852-x.

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Kapovitch, Vitali, et Christian Ketterer. « Weakly Noncollapsed RCD Spaces with Upper Curvature Bounds ». Analysis and Geometry in Metric Spaces 7, n^o 1 (1 janvier 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 (janvier 2021) : 163–203. http://dx.doi.org/10.1016/j.matpur.2020.07.004.

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11

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

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12

Gigli, Nicola, et Luca Tamanini. « Second order differentiation formula on RCD*$(K,N)$ spaces ». Journal of the European Mathematical Society 23, n^o 5 (2 février 2021) : 1727–95. http://dx.doi.org/10.4171/jems/1042.

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Gigli, Nicola. « Lecture Notes On Differential Calculus on $\mathscr {RCD}$ Spaces ». Publications of the Research Institute for Mathematical Sciences 54, n^o 4 (18 octobre 2018) : 855–918. http://dx.doi.org/10.4171/prims/54-4-4.

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14

Gigli, Nicola, Christian Ketterer, Kazumasa Kuwada et Shin-Ichi Ohta. « Rigidity for the spectral gap on Rcd(K, ∞)-spaces ». American Journal of Mathematics 142, n^o 5 (2020) : 1559–94. http://dx.doi.org/10.1353/ajm.2020.0039.

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15

Brué, Elia, et Daniele Semola. « Regularity of Lagrangian flows over RCD*(K, N) spaces ». Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, n^o 765 (1 août 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, et Luca Tamanini. « Second order differentiation formula on RCD$(K,N)$ spaces ». Rendiconti Lincei - Matematica e Applicazioni 29, n^o 2 (26 avril 2018) : 377–86. http://dx.doi.org/10.4171/rlm/811.

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17

Gigli, Nicola, et Enrico Pasqualetto. « On the notion of parallel transport on RCD spaces ». Revista Matemática Iberoamericana 36, n^o 2 (17 décembre 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, n^o 7 (juillet 2019) : 613–19. http://dx.doi.org/10.1016/j.crma.2019.06.003.

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19

Gigli, Nicola, et Chiara Rigoni. « A Note About the Strong Maximum Principle on RCD Spaces ». Canadian Mathematical Bulletin 62, n^o 02 (7 janvier 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, n^o 6 (20 novembre 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, n^o 1 (1 octobre 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 et David Tewodrose. « Embedding of RCD⁎(K,N) spaces in L2 via eigenfunctions ». Journal of Functional Analysis 280, n^o 10 (mai 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, n^o 10 (2018) : 4915–27. http://dx.doi.org/10.3934/dcds.2018214.

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24

Bruè, Elia, Enrico Pasqualetto et Daniele Semola. « Rectifiability of RCD(K,N) spaces via δ-splitting maps ». Annales Fennici Mathematici 46, n^o 1 (juin 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, n^o 4 (29 mai 2015) : 1280–97. http://dx.doi.org/10.1007/s10959-015-0621-0.

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26

Gigli, Nicola, et Bang-Xian Han. « Independence on p of weak upper gradients on RCD spaces ». Journal of Functional Analysis 271, n^o 1 (juillet 2016) : 1–11. http://dx.doi.org/10.1016/j.jfa.2016.04.014.

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27

Zhang, Hui-Chun, et Xi-Ping Zhu. « Weyl’s law on $RCD^{\ast} (K, N)$ metric measure spaces ». Communications in Analysis and Geometry 27, n^o 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, n^o 2 (novembre 2019) : 1618–40. http://dx.doi.org/10.1016/j.jmaa.2019.07.015.

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29

Gigli, Nicola, et 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, n^o 1-2 (30 avril 2019) : 1–34. http://dx.doi.org/10.1007/s00440-019-00909-1.

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30

Kemper, Matthias, et Joachim Lohkamp. « Potential Theory on Gromov Hyperbolic Spaces ». Analysis and Geometry in Metric Spaces 10, n^o 1 (1 janvier 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 et 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, n^o 1 (15 août 2017) : 97–119. http://dx.doi.org/10.1007/s10455-017-9569-x.

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32

De Ponti, Nicolò, Andrea Mondino et Daniele Semola. « The equality case in Cheeger's and Buser's inequalities on RCD spaces ». Journal of Functional Analysis 281, n^o 3 (août 2021) : 109022. http://dx.doi.org/10.1016/j.jfa.2021.109022.

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33

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

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34

Gigli, Nicola, et Enrico Pasqualetto. « Behaviour of the reference measure on $\mathsf{RCD}$ spaces under charts ». Communications in Analysis and Geometry 29, n^o 6 (2021) : 1391–414. http://dx.doi.org/10.4310/cag.2021.v29.n6.a3.

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35

Han, Bang-Xian, et Andrea Mondino. « Angles between Curves in Metric Measure Spaces ». Analysis and Geometry in Metric Spaces 5, n^o 1 (2 septembre 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 et Daniele Semola. « Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces ». Analysis and Geometry in Metric Spaces 7, n^o 1 (1 janvier 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, et 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, n^o 3-4 (6 décembre 2018) : 303–24. http://dx.doi.org/10.1007/s00229-018-1095-z.

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38

Kapovitch, Vitali, et Andrea Mondino. « On the topology and the boundary of N–dimensional RCD(K,N) spaces ». Geometry & ; Topology 25, n^o 1 (2 mars 2021) : 445–95. http://dx.doi.org/10.2140/gt.2021.25.445.

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39

Ambrosio, Luigi, et Andrea Mondino. « Gaussian-type isoperimetric inequalities in RCD $(K, \infty)$ probability spaces for positive $K$ ». Rendiconti Lincei - Matematica e Applicazioni 27, n^o 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, n^o 12 (4 septembre 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, n^o 1 (9 février 2019) : 315–28. http://dx.doi.org/10.1007/s11118-019-09770-2.

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42

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

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43

Guijarro, Luis, et Jaime Santos-Rodríguez. « On the isometry group of $$RCD^*(K,N)$$ R C D ∗ ( K , N ) -spaces ». manuscripta mathematica 158, n^o 3-4 (5 mars 2018) : 441–61. http://dx.doi.org/10.1007/s00229-018-1010-7.

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44

Brué, Elia, et Daniele Semola. « Constancy of the Dimension for RCD( K , N ) Spaces via Regularity of Lagrangian Flows ». Communications on Pure and Applied Mathematics 73, n^o 6 (juin 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, n^o 04 (13 décembre 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 et 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, n^o 1 (7 octobre 2014) : 24–56. http://dx.doi.org/10.1007/s12220-014-9537-7.

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47

Ambrosio, Luigi, Elia Brué et Daniele Semola. « Rigidity of the 1-Bakry–Émery Inequality and Sets of Finite Perimeter in RCD Spaces ». Geometric and Functional Analysis 29, n^o 4 (1 juillet 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, n^o 3-4 (9 février 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, n^o 04 (28 août 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, n^o 4 (2014) : 1641–61. http://dx.doi.org/10.3934/dcds.2014.34.1641.

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Articles de revues sur le sujet « RCD spaces »

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