Interior C2 regularity of convex solutions to prescribing scalar curvature equations

By Pengfei Guan, Guohuan Qiu. Duke mathematical journal, 2017

63 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/cd0c53fdd3ba78381ab64c7f0c1e8f300eef02d3