Local $C^0$-estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds
Differential Geometry
2021-01-14 v1 Analysis of PDEs
Abstract
In this article we study a class of prescribed curvature problems on complete noncompact Riemannian manifolds. To be precise, we derive local -estimate under an asymptotic condition which is in effect optimal, and prove the existence of complete conformal metrics with prescribed curvature functions. A key ingredient of our strategy is Aviles-McOwen's result or its fully nonlinear version on the existence of complete conformal metrics with prescribed curvature functions on manifolds with boundary.
Keywords
Cite
@article{arxiv.2101.04947,
title = {Local $C^0$-estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds},
author = {Rirong Yuan},
journal= {arXiv preprint arXiv:2101.04947},
year = {2021}
}