Global C2‐Estimates for Convex Solutions of Curvature Equations

2014/07/08 by Pengfei Guan, Changyu Ren, Zhizhang Wang · 115 citations
Mathematics · #A priori and a posteriori #Curvature #Elliptic curve #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematics #Mean curvature #Nonlinear Partial Differential Equations #Nonlinear system #Numerical methods in inverse problems #Physics #Principal (computer security) #Principal curvature #Pure mathematics #Regular polygon

paper · doi:10.1002/cpa.21528

published in Communications on Pure and Applied Mathematics 68(8), 1287-1325 (Wiley)

openalex publication_date 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

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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