Rigidity theorems on conformal class of compact manifolds with boundary

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:437

Article

Barbosa, Ezequiel^1,4  Mirandola, Heudson.^2,4  Vitorio, Feliciano³ 

[1] Univ Fed Minas Gerais, Inst Ciencias Exatas, BR-31270901 Belo Horizonte, MG, Brazil

[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21945970 Rio De Janeiro, RJ, Brazil

[3] Univ Fed Alagoas, Inst Matemat, BR-57072900 Maceio, Al, Brazil

[4] Univ London Imperial Coll Sci Technol & Med, Huxley Bldg,180 Queens Gate, London SW7 2RH, England

关键词: Static metrics;    Conformal class;    Rigidity theorems;    Min-Oo problem;    Scalar curvature;    Mean curvature;   

DOI  :  10.1016/j.jmaa.2016.01.006

来源: Elsevier

【 摘 要 】

Let M be a compact manifold with boundary. In this paper, we discuss some rigidity theorems on Riemannian metrics in a same conformal class that fix the boundary and satisfy certain integral condition on the scalar curvature and on the mean curvature along the boundary. As an application, we will state some rigidity theorems on the conformal class of static metrics. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free