The boundary value Minkowski problem for Weingarten curvatures
Differential Geometry
2018-10-03 v1 Analysis of PDEs
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.
Cite
@article{arxiv.1810.01010,
title = {The boundary value Minkowski problem for Weingarten curvatures},
author = {Flávio França Cruz},
journal= {arXiv preprint arXiv:1810.01010},
year = {2018}
}
Comments
14 pages