Curvature estimates for $p$-convex hypersurfaces of prescribed curvature

Weisong Dong

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arXiv · 2107.13387

Curvature estimates for $p$-convex hypersurfaces of prescribed curvature

Weisong Dong

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Abstract

In this paper, we establish the curvature estimates for $p$-convex hypersurfaces in $\mathbb{R}^{n+1}$ of prescribed curvature with $p\geq \frac{n}{2}$. The existence of a star-shaped hypersurface of prescribed curvature is obtained. We also prove a type of interior $C^2$ estimates for solutions to the Dirichlet problem of the corresponding equation.

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Weisong Dong. 2022-04-28. Curvature estimates for $p$-convex hypersurfaces of prescribed curvature. https://arxiv.org/abs/2107.13387

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