Prescribed curvature measure problem in hyperbolic space

Fengrui Yang

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arXiv · 2008.09729

Prescribed curvature measure problem in hyperbolic space

Fengrui Yang

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Abstract

The problem of the prescribed curvature measure is one of the important problems in differential geometry and nonlinear partial differential equations. In this paper, we consider prescribed curvature measure problem in hyperbolic space. We obtain the existence of star-shaped k-convex bodies with prescribed (n-k)-th curvature measures (k<n) by establishing crucial C^2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.

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Fengrui Yang. 2020-08-22. Prescribed curvature measure problem in hyperbolic space. https://arxiv.org/abs/2008.09729

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