Rigidity theorems on conformal class of compact manifolds with boundary

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• 作者：Ezequiel Barbosa^a ; ¹ ; ^{ezequiel@mat.ufmg.br" class="auth_mail" title="E-mail the corresponding author} ; Heudson Mirandola^b ; ¹ ; ^{mirandola@im.ufrj.br" class="auth_mail" title="E-mail the corresponding author} ; Feliciano Vitorio^c ; ^{feliciano@pos.mat.ufal.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Static metrics ; Conformal class ; Rigidity theorems ; Min-Oo problem ; Scalar curvature ; Mean curvature
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：629-637
• 全文大小：291 K

文摘

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.