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arXiv · 2511.01130

Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds

Weisong Dong·Yanyan Li·Luc Nguyen
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Abstract

In this paper, we consider the Dirichlet boundary value problem for fully nonlinear Yamabe equations on Riemannian manifolds with boundary. Assuming the existence of a subsolution, we derive \emph{a priori} boundary second derivative estimates and consequently obtain the existence of a smooth solution. Moreover, with respect to a family of equations interpolating the fully nonlinear Yamabe equation and the classical semi-linear Yamabe equation, our estimates remain uniform. Finally, an example of a $C^1$ solution which is smooth in the interior but not smooth at the boundary is also given.

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Weisong Dong, Yanyan Li, Luc Nguyen. 2025-11-03. Boundary estimates for a fully nonlinear Yamabe problem on Riemannian manifolds. https://arxiv.org/abs/2511.01130

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