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arXiv · 2410.06302

Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature

Jiashu Shen·Hongyi Sheng
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Abstract

Let $(M, g)$ be a compact Riemannian manifold with boundary $\partial M$. Given a function $f$ on $\partial M$, we consider the problem of finding a conformal metric of $g$ with zero scalar curvature in $M$ and prescribed mean curvature $f$ on $\partial M$. Through the construction of local test functions, we resolve most of the remaining open cases from Escobar's work and establish new solvability conditions.

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Jiashu Shen, Hongyi Sheng. 2024-10-08. Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature. https://doi.org/10.1007/s00209-026-04060-1

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