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arXiv · 1711.00932

Interior C2 regularity of convex solutions to prescribing scalar curvature equations

Pengfei Guan·Guohuan Qiu
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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.

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Pengfei Guan, Guohuan Qiu. 2017-11-02. Interior C2 regularity of convex solutions to prescribing scalar curvature equations. https://doi.org/10.1215/00127094-2019-0001

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