The Dirichlet problem for prescribed curvature equations of $p$-convex hypersurfaces

Weisong Dong

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arXiv · 2208.09794

The Dirichlet problem for prescribed curvature equations of $p$-convex hypersurfaces

Weisong Dong

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Abstract

In this paper, we study the Dirichlet problem for $p$-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.

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Weisong Dong. 2022-08-21. The Dirichlet problem for prescribed curvature equations of $p$-convex hypersurfaces. https://arxiv.org/abs/2208.09794

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