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

被引：1

作者：

Almaraz, Sergio ^{[1
]}

Wang, Shaodong ^{[2
]}

机构：

[1] Univ Fed Fluminense, Inst Matemat & Estat, Rua Prof Marcos Waldemar Freitas S-N, BR-24210201 Niteroi, RJ, Brazil

[2] Nanjing Univ Sci & Technol, Sch Math & Stat, Nanjing 210094, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2025年 / 64卷 / 01期

关键词：

BLOW-UP PHENOMENA; YAMABE PROBLEM; FLAT METRICS; UNIQUENESS THEOREMS; EXISTENCE THEOREM; MANIFOLDS; DEFORMATION; EQUATION; PROOF;

D O I：

10.1007/s00526-024-02895-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：24

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