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

2023/06/12 by Almaraz, Sergio, Wang, Shaodong · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.07088

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.

Cited by

• Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)

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