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.
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页数：24
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