A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three

Sergio Almaraz; Shaodong Wang

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arXiv · 2306.07088

A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three

Sergio Almaraz·Shaodong Wang

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Abstract

On a compact three-dimensional Riemannian manifold with boundary, we prove the compactness of the full set of conformal metrics with positive constant scalar curvature and constant mean curvature on the boundary. This involves a blow-up analysis of a Yamabe equation with critical Sobolev exponents both in the interior and on the boundary.

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Sergio Almaraz, Shaodong Wang. 2023-06-12. A compactness theorem for conformal metrics with constant scalar curvature and constant boundary mean curvature in dimension three. https://arxiv.org/abs/2306.07088

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