On the prescribed negative Gauss curvature problem for graphs

DOI10.3934/DCDS.2022133arXiv2209.02326OpenAlexW4296280846MaRDI QIDQ6102547

Christoph Kehle, Alessio Figalli

Publication date: 23 June 2023

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2209.02326

zbMATH Keywords

energy estimatesNash-Moser iterationhyperbolic Monge-Ampère equationLorentzian metricprescribed negative Gauss curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Hyperbolic equations on manifolds (58J45) Monge-Ampère equations (35J96)

Cites Work

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• Smooth solutions to a class of mixed type Monge-Ampère equations
• The Monge-Ampère equation and its applications
• Local solutions to a class of Monge-Ampère equations of mixed type
• Realization in \(\mathbb{R}^ 3\) of complete Riemannian manifolds with negative curvature
• Smooth local solutions to degenerate hyperbolic Monge-Ampère equations
• The inverse function theorem of Nash and Moser

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