A simple proof of curvature estimate for convex solution of 𝑘-Hessian equation

DOI10.1090/proc/15408zbMath1471.53007arXiv2003.00634OpenAlexW3111284075MaRDI QIDQ4992936

Jianchun Chu

Publication date: 10 June 2021

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.00634

zbMATH Keywords

principal curvaturesWeingarten curvature equation\(k\)-th elementary symmetric function

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (3)

On the asymptotic Plateau problem in hyperbolic space ⋮ The global curvature estimate for the \(n - 2\) Hessian equation ⋮ Curvature estimates for semi-convex solutions of Hessian equations in hyperbolic space

Cites Work

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• Hypersurfaces of prescribed curvature measure
• A note on star-shaped compact hypersurfaces with prescribed scalar curvature in space forms
• Embedded hyperspheres with prescribed mean curvature
• Closed Weingarten hypersurfaces in Riemannian manifolds
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• Convex hypersurfaces of prescribed curvatures
• SOLUTION OF THE DIRICHLET PROBLEM FOR CURVATURE EQUATIONS OF ORDER $ m$
• The Existence of Convex Body with Prescribed Curvature Measures
• The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
• On the regularity of the solution of then-dimensional Minkowski problem
• A variational theory of the Hessian equation
• On the curvature estimates for Hessian equations
• Global C²‐Estimates for Convex Solutions of Curvature Equations
• The Weyl and Minkowski problems in differential geometry in the large

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