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Relevant bibliographies by topics / Complex Monge Ampere / Journal articles

Journal articles on the topic 'Complex Monge Ampere'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Semmes, Stephen. "Complex Monge-Ampere and Symplectic Manifolds." American Journal of Mathematics 114, no. 3 (June 1992): 495. http://dx.doi.org/10.2307/2374768.

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2

Do, Hoang son. "Weak solution of Parabolic complex Monge-Ampere equation." Indiana University Mathematics Journal 66, no. 6 (2017): 1949–79. http://dx.doi.org/10.1512/iumj.2017.66.6186.

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3

Chen, Xiuxiong, and Gang Tian. "Partial regularity for homogeneous complex Monge–Ampere equations." Comptes Rendus Mathematique 340, no. 5 (March 2005): 337–40. http://dx.doi.org/10.1016/j.crma.2004.11.024.

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4

Moriyón, Roberto. "The degenerate complex monge-ampere equation on thin annuli." Communications in Partial Differential Equations 11, no. 11 (January 1986): 1205–42. http://dx.doi.org/10.1080/03605308608820461.

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5

Phong, D. H., and Jacob Sturm. "The Dirichlet problem for degenerate complex Monge–Ampere equations." Communications in Analysis and Geometry 18, no. 1 (2010): 145–70. http://dx.doi.org/10.4310/cag.2010.v18.n1.a6.

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6

Kolodziej, Slawomir. "The range of the complex Monge-Ampere operator II." Indiana University Mathematics Journal 44, no. 3 (1995): 0. http://dx.doi.org/10.1512/iumj.1995.44.2007.

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7

Blocki, Zbigniew. "The domain of definition of the complex Monge-Ampere operator." American Journal of Mathematics 128, no. 2 (2006): 519–30. http://dx.doi.org/10.1353/ajm.2006.0010.

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8

Dinew, Slawomir, Xi Zhang, and XiangWen Zhang. "The $\mathcal C^{2,\alpha}$ estimate of complex Monge-Ampere equation." Indiana University Mathematics Journal 60, no. 5 (2011): 1713–22. http://dx.doi.org/10.1512/iumj.2011.60.4444.

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9

Koeodziej, Slawomir. "Regularity of the Entire Solutions to the Complex Monge-Ampere Equation." Communications in Analysis and Geometry 12, no. 5 (2004): 1173–84. http://dx.doi.org/10.4310/cag.2004.v12.n5.a9.

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10

Åhag, Per, Urban Cegrell, and Rafal Czyz. "On Dirichlet's principle and problem." MATHEMATICA SCANDINAVICA 110, no. 2 (June 1, 2012): 235. http://dx.doi.org/10.7146/math.scand.a-15206.

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The aim of this paper is to give a new proof of the complete characterization of measures for which there exists a solution of the Dirichlet problem for the complex Monge-Ampere operator in the set of plurisubharmonic functions with finite pluricomplex energy. The proof uses variational methods.

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11

Xing, Yang. "The complex Monge-Ampere equations with a countable number of singular points." Indiana University Mathematics Journal 48, no. 2 (1999): 0. http://dx.doi.org/10.1512/iumj.1999.48.1663.

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12

Chen, Xiuxiong, and Yuanqi Wang. "On the regularity problem of complex Monge–Ampere equations with conical singularities." Annales de l’institut Fourier 67, no. 3 (2017): 969–1003. http://dx.doi.org/10.5802/aif.3102.

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13

Blocki, Zbigniew. "Uniqueness and stability for the complex Monge-Ampere equation on compact Kahler manifolds." Indiana University Mathematics Journal 52, no. 6 (2003): 1697–702. http://dx.doi.org/10.1512/iumj.2003.52.2346.

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14

Monn, David. "Regularity of the complex monge-ampere equation for radially symmetric functions of the unit ball." Mathematische Annalen 275, no. 3 (September 1986): 501–11. http://dx.doi.org/10.1007/bf01458619.

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15

Kruglikov, B. S. "Some classification problems in four-dimensional geometry: distributions, almost complex structures, and generalized Monge-Ampere equations." Sbornik: Mathematics 189, no. 11 (December 31, 1998): 1643–56. http://dx.doi.org/10.1070/sm1998v189n11abeh000370.

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16

Phong, D. H., Jian Song, and Jacob Sturm. "Complex Monge-Ampère equations." Surveys in Differential Geometry 17, no. 1 (2012): 327–410. http://dx.doi.org/10.4310/sdg.2012.v17.n1.a8.

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17

Czyż, Rafał. "The complex Monge–Ampère operator." Dissertationes Mathematicae 466 (2009): 1–83. http://dx.doi.org/10.4064/dm466-0-1.

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18

Kołodziej, Sławomir. "The complex Monge-Ampère equation." Acta Mathematica 180, no. 1 (1998): 69–117. http://dx.doi.org/10.1007/bf02392879.

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19

Hou, Zuoliang, and Qi Li. "Energy Functionals and Complex Monge–Ampère Equations." Journal of the Institute of Mathematics of Jussieu 9, no. 3 (February 10, 2010): 463–76. http://dx.doi.org/10.1017/s1474748009000206.

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AbstractWe introduce certain energy functionals to complex Monge–Ampère equations over bounded domains with inhomogeneous boundary conditions, and use these functionals to show the convergence of solutions to certain parabolic Monge–Ampère equations.

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20

Bedford, Eric, and Sione Ma`u. "Complex Monge-Ampère of a maximum." Proceedings of the American Mathematical Society 136, no. 01 (January 1, 2008): 95–102. http://dx.doi.org/10.1090/s0002-9939-07-09145-9.

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21

Banos, Bertrand. "Complex solutions of Monge–Ampère equations." Journal of Geometry and Physics 61, no. 11 (November 2011): 2187–98. http://dx.doi.org/10.1016/j.geomphys.2011.06.019.

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22

Fu, Xin, Bin Guo, and Jian Song. "Geometric estimates for complex Monge–Ampère equations." Journal für die reine und angewandte Mathematik (Crelles Journal) 2020, no. 765 (August 1, 2020): 69–99. http://dx.doi.org/10.1515/crelle-2019-0020.

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AbstractWe prove uniform gradient and diameter estimates for a family of geometric complex Monge–Ampère equations. Such estimates can be applied to study geometric regularity of singular solutions of complex Monge–Ampère equations. We also prove a uniform diameter estimate for collapsing families of twisted Kähler–Einstein metrics on Kähler manifolds of nonnegative Kodaira dimensions.

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23

GUEDJ, Vincent, Chinh H. LU, and Ahmed ZERIAHI. "Weak subsolutions to complex Monge–Ampère equations." Journal of the Mathematical Society of Japan 71, no. 3 (July 2019): 727–38. http://dx.doi.org/10.2969/jmsj/79677967.

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24

Xing, Yang. "A decomposition of complex Monge–Ampère measures." Annales Polonici Mathematici 92, no. 2 (2007): 191–95. http://dx.doi.org/10.4064/ap92-2-7.

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25

Spiliotis, J. "A Complex Parabolic Type MongeAmpère Equation." Applied Mathematics and Optimization 35, no. 3 (May 1, 1997): 265–82. http://dx.doi.org/10.1007/s002459900048.

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26

Tô, Tat Dat. "Regularizing properties of complex Monge–Ampère flows." Journal of Functional Analysis 272, no. 5 (March 2017): 2058–91. http://dx.doi.org/10.1016/j.jfa.2016.10.017.

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27

Xing, Yang. "Continuity of the complex Monge-Ampère operator." Proceedings of the American Mathematical Society 124, no. 2 (1996): 457–67. http://dx.doi.org/10.1090/s0002-9939-96-03316-3.

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28

Spiliotis, J. "A complex parabolic type monge-ampère equation." Applied Mathematics & Optimization 35, no. 3 (May 1997): 265–82. http://dx.doi.org/10.1007/bf02683331.

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29

Wei, Wang. "Complex Monge-Ampère equations on general domains." Applied Mathematics-A Journal of Chinese Universities 16, no. 3 (September 2001): 268–78. http://dx.doi.org/10.1007/s11766-001-0065-4.

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30

Xing, Yang. "Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary." Canadian Journal of Mathematics 52, no. 5 (October 1, 2000): 1085–100. http://dx.doi.org/10.4153/cjm-2000-045-x.

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AbstractWe give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.

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31

Hai, Le Mau, Tang Van Long, and Trieu Van Dung. "Equations of complex Monge–Ampère type for arbitrary measures and applications." International Journal of Mathematics 27, no. 04 (April 2016): 1650035. http://dx.doi.org/10.1142/s0129167x1650035x.

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In this paper, we prove the existence of weak solutions of equations of complex Monge–Ampère type for arbitrary measures, in particular, measures carried by pluripolar sets. As an application of the obtained result, we show the existence of weak solutions of equations of complex Monge–Ampère type in the class [Formula: see text] if there exist locally subsolutions.

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32

Einstein-Matthews, Stanley M. "Symplectic structures and symmetries of solutions of the complex Monge-Ampére equation." Nagoya Mathematical Journal 150 (June 1998): 63–83. http://dx.doi.org/10.1017/s0027763000025058.

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Abstract.The graphs that arise from the gradients of solutions u of the homogeneous complex Monge-Ampère equation are characterized in terms of the natural symplectic structure on the cotangent bundle. This characterization is invariant under symplectic biholomorphisms. Using the symplectic structures we construct symmetries (to be called Lempert transformations) for real valued functions u which are absolutely continuous on lines. We then use these symmetries to generate interesting solutions to the homogeneous complex Monge-Ampère equation and to transform the Poincaré-Lelong equation and the ∂-equation. An example of Lempert transform is given and the main theorem is applied to prove regularity results for exterior nonlinear Dirichlet problem for the homogeneous complex Monge-Ampère equation.

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33

Celik, Halil, and Evgeny Poletsky. "Fundamental solutions of the complex Monge-Ampère equation." Annales Polonici Mathematici 67, no. 2 (1997): 103–10. http://dx.doi.org/10.4064/ap-67-2-103-110.

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34

Wiklund, Jonas. "Matrix inequalities and the complex Monge–Ampère operator." Annales Polonici Mathematici 83, no. 3 (2004): 211–20. http://dx.doi.org/10.4064/ap83-3-3.

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35

Li, Chao, Jiayu Li, and Xi Zhang. "AC2,αestimate of the complex Monge–Ampère equation." Journal of Functional Analysis 275, no. 1 (July 2018): 149–69. http://dx.doi.org/10.1016/j.jfa.2018.01.020.

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36

Berman, Robert J., Sébastien Boucksom, Vincent Guedj, and Ahmed Zeriahi. "A variational approach to complex Monge-Ampère equations." Publications mathématiques de l'IHÉS 117, no. 1 (November 14, 2012): 179–245. http://dx.doi.org/10.1007/s10240-012-0046-6.

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37

Guan, Bo, and Qun Li. "Complex Monge–Ampère equations and totally real submanifolds." Advances in Mathematics 225, no. 3 (October 2010): 1185–223. http://dx.doi.org/10.1016/j.aim.2010.03.019.

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38

Hai, Le Mau, and Pham Hoang Hiep. "An equality on the complex Monge–Ampère measures." Journal of Mathematical Analysis and Applications 444, no. 1 (December 2016): 503–11. http://dx.doi.org/10.1016/j.jmaa.2016.06.023.

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39

Guedj, Vincent, Chinh H. Lu, and Ahmed Zeriahi. "Stability of solutions to complex Monge–Ampère flows." Annales de l'Institut Fourier 68, no. 7 (2018): 2819–36. http://dx.doi.org/10.5802/aif.3227.

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40

Kołodziej, Sławomir. "The complex Monge-Ampère equation and pluripotential theory." Memoirs of the American Mathematical Society 178, no. 840 (2005): 0. http://dx.doi.org/10.1090/memo/0840.

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41

Do, Hoang-Son, Thai Duong Do, and Hoang Hiep Pham. "Complex Monge-Ampère Equation in Strictly Pseudoconvex Domains." Acta Mathematica Vietnamica 45, no. 1 (February 19, 2019): 93–101. http://dx.doi.org/10.1007/s40306-018-00313-2.

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42

Pliś, Szymon. "The Monge–Ampère equation on almost complex manifolds." Mathematische Zeitschrift 276, no. 3-4 (October 18, 2013): 969–83. http://dx.doi.org/10.1007/s00209-013-1229-7.

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43

Eyssidieux, Philippe, Vincent Guedj, and Ahmed Zeriahi. "Viscosity solutions to degenerate complex monge-ampère equations." Communications on Pure and Applied Mathematics 64, no. 8 (March 14, 2011): 1059–94. http://dx.doi.org/10.1002/cpa.20364.

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44

Eyssidieux, Philippe, Vincent Guedj, and Ahmed Zeriahi. "Corrigendum: Viscosity Solutions to Complex Monge-Ampère Equations." Communications on Pure and Applied Mathematics 70, no. 5 (March 17, 2017): 815–21. http://dx.doi.org/10.1002/cpa.21692.

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45

Benelkourchi, Slimane. "Weighted Pluricomplex Energy II." International Journal of Partial Differential Equations 2015 (February 10, 2015): 1–8. http://dx.doi.org/10.1155/2015/947819.

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We continue our study of the complex Monge-Ampère operator on the weighted pluricomplex energy classes. We give more characterizations of the range of the classes Eχ by the complex Monge-Ampère operator. In particular, we prove that a nonnegative Borel measure μ is the Monge-Ampère of a unique function φ∈Eχ if and only if χ(Eχ)⊂L1(dμ). Then we show that if μ=(ddcφ)n for some φ∈Eχ then μ=(ddcu)n for some φ∈Eχ, where f is given boundary data. If moreover the nonnegative Borel measure μ is suitably dominated by the Monge-Ampère capacity, we establish a priori estimates on the capacity of sublevel sets of the solutions. As a consequence, we give a priori bounds of the solution of the Dirichlet problem in the case when the measure has a density in some Orlicz space.

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46

Czyż, Rafał. "The complex Monge–Ampère equation for complex homogeneous functions in Cn." Annales Polonici Mathematici 76, no. 3 (2001): 287–302. http://dx.doi.org/10.4064/ap76-3-7.

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47

Cegrell, Urban, and Leif Persson. "An energy estimate for the complex Monge-Ampère operator." Annales Polonici Mathematici 67, no. 1 (1997): 95–102. http://dx.doi.org/10.4064/ap-67-1-95-102.

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48

Kołodziej, Sławomir. "Weak solutions of equations of complex Monge-Ampère type." Annales Polonici Mathematici 73, no. 1 (2000): 59–67. http://dx.doi.org/10.4064/ap-73-1-59-67.

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49

Charabati, Mohamad. "Hölder regularity for solutions to complex Monge–Ampère equations." Annales Polonici Mathematici 113, no. 2 (2015): 109–27. http://dx.doi.org/10.4064/ap113-2-1.

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50

Åhag, Per, and Rafał Czyż. "On the complex Monge-Ampère operator in unbounded domains." Acta Mathematica 54 (2017): 7–13. http://dx.doi.org/10.4467/20843828am.17.001.7077.

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