Prescribed curvature measure problem in hyperbolic space
Analysis of PDEs
2020-08-25 v1 Differential Geometry
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.
Cite
@article{arxiv.2008.09729,
title = {Prescribed curvature measure problem in hyperbolic space},
author = {Fengrui Yang},
journal= {arXiv preprint arXiv:2008.09729},
year = {2020}
}