Prescribed curvature measure problem in hyperbolic space-Reference-Cited by-同舟云学术

Prescribed curvature measure problem in hyperbolic space

Published:2023-09-07 Issue:1 Volume:77 Page:863-898
ISSN:0010-3640
Container-title:Communications on Pure and Applied Mathematics
language:en
Short-container-title:Comm Pure Appl Math

Author:

Yang Fengrui¹

Affiliation:

1. McGill University Montreal Canada

Abstract

AbstractThe 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 the prescribed curvature measure problem in the hyperbolic space. We obtain the existence of star‐shaped k‐convex bodies with prescribed (n‐k)‐th curvature measures by establishing crucial C2 regularity estimates for solutions to the corresponding fully nonlinear PDE in the hyperbolic space.

Publisher

Wiley

Subject

Applied Mathematics,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.22160

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