Hölder continuous solutions to Monge-Ampère equations

DOI10.4171/JEMS/442zbMath1296.32012arXiv1112.1388WikidataQ125825032 ScholiaQ125825032MaRDI QIDQ2449821

Sławomir Dinew, Sławomir Kołodziej, Jean-Pierre Demailly, Ahmed Zeriahi, Vincent Guedj, Phạm Hoàng Hiệp

Publication date: 12 May 2014

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.1388

zbMATH Keywords

Kähler manifoldHölder continuitypluripotential theoryMonge-Ampère operator

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Plurisubharmonic functions and generalizations (32U05) Currents (32U40)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Monge-Ampère equations in big cohomology classes
• A new capacity for plurisubharmonic functions
• On stability and continuity of bounded solutions of degenerate complex Monge-Ampère equations over compact Kähler manifolds
• Exponential estimates for plurisubharmonic functions
• The Dirichlet problem for a complex Monge-Ampère equation
• A thermodynamical formalism for Monge-Ampère equations, Moser-Trudinger inequalities and Kähler-Einstein metrics
• Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes
• Hölder continuous potentials on manifolds with partially positive curvature
• A priori estimates for weak solutions of complex Monge-Amp\`ere equations
• DEGENERATE COMPLEX MONGE–AMPÈRE EQUATIONS OVER COMPACT KÄHLER MANIFOLDS
• Existence of minimal models for varieties of log general type
• Estimations $\mathrm{L}^2$ pour l'opérateur $\bar \partial$ d'un fibré vectoriel holomorphe semi-positif au-dessus d'une variété kählérienne complète

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