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arXiv · 1310.4730

Starshaped locally convex hypersurfaces with prescribed curvature and boundary

Chenyang Su
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Abstract

In this paper we find strictly locally convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed curvature and boundary. The main result is that if the given data admits a strictly locally convex radial graph as a subsolution, we can find a radial graph realizing the prescribed curvature and boundary. As an application we show any smooth domain on the boundary of a compact strictly convex body can be deformed to a smooth hypersurface with the same boundary (inside the convex body) and realizing any prescribed curvature function smaller than the curvature of the body.

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Chenyang Su. 2013-10-17. Starshaped locally convex hypersurfaces with prescribed curvature and boundary. https://doi.org/10.1007/s12220-015-9606-6

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