Global C2‐Estimates for Convex Solutions of Curvature Equations

2014/07/08 by Pengfei Guan, Changyu Ren, Zhizhang Wang · 14 citations
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · doi:10.1002/cpa.21528

Abstract

We establish a C 2 a priori estimate for convex hypersurfaces whose principal curvatures κ=(κ 1 ,…, κ n ) satisfy σ k (κ( X ))= f ( X ,ν( X )), the Weingarten curvature equation. We also obtain such an estimate for admissible 2‐convex hypersurfaces in the case k =2. Our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations.© 2015 Wiley Periodicals, Inc.

Citations

• Convexity estimates for mean curvature flow and singularities of mean convex surfaces

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