Interior C2 regularity of convex solutions to prescribing scalar curvature equations

Abstract

We establish interior $C^2$ estimates for convex solutions of scalar curvature equation and ${\sigma }_2$-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces $(M^n,g)\subset {\mathbb{R}}^{n+1}$ with positive scalar curvature. These estimates are consequences of an interior estimate for these equations obtained under a weakened condition.

16 pages

References in corpus (2)

• Curvature estimates for immersed hypersurfaces in Riemannian manifolds
• The interior $C^2$ estimate for Monge-Ampere equation in dimension $n=2$

Cited by in corpus (5)

• Hessian Estimates for Lagrangian mean curvature equation
• Interior curvature estimates for hypersurfaces of prescribing scalar curvature in dimension three
• Convex Hypersurfaces with Prescribed Scalar Curvature and Asymptotic Boundary in Hyperbolic Space
• Rigidity of the entire solutions of 2-Hessian equation
• Lipschitz Continuous Hypersurfaces with Prescribed Curvature and Asymptotic Boundary in Hyperbolic Space