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arXiv · 2101.04947

Local $C^0$-estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds

Rirong Yuan
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Abstract

In this article we study a class of prescribed curvature problems on complete noncompact Riemannian manifolds. To be precise, we derive local $C^0$-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.

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Rirong Yuan. 2021-01-13. Local $C^0$-estimate and existence theorems for some prescribed curvature problems on complete noncompact Riemannian manifolds. https://arxiv.org/abs/2101.04947

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