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arXiv · 1810.01010

The boundary value Minkowski problem for Weingarten curvatures

Flávio França Cruz
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Abstract

In this paper, we prove the existence of hypersurfaces in the Euclidean space with prescribed boundary and whose k-th Weingarten curvature equals a given function that depends on the normal of the hypersurface. The proof is based on the solvability of a fully nonlinear elliptic PDE. The required a priori estimates are established under the natural assumptions that the prescribed boundary is strictly convex and the prescribed function satisfies a Serrin type condition.

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Flávio França Cruz. 2018-10-01. The boundary value Minkowski problem for Weingarten curvatures. https://arxiv.org/abs/1810.01010

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