Global C2‐Estimates for Convex Solutions of Curvature Equations |
| |
| Authors: | Pengfei Guan Changyu Ren Zhizhang Wang |
| |
| Institution: | 1. Department of Mathematics and Statistics, McGill University, Montreal, Canada;2. School of Mathematical Science, Jilin University, Changchun, China |
| |
| Abstract: | We establish a C2 a priori estimate for convex hypersurfaces whose principal curvatures κ=(κ1,…, κn) satisfy σk(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. |
| |
| Keywords: | |
|
|
