Prescribed curvature measure problem in hyperbolic space
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 C2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.
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