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Critical metrics of the volume functional on compact three-manifolds with smooth boundary

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 نشر من قبل Ernani Ribeiro Jr
 تاريخ النشر 2016
  مجال البحث
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We study the space of smooth Riemannian structures on compact three-manifolds with boundary that satisfies a critical point equation associated with a boundary value problem, for simplicity, Miao-Tam critical metrics. We provide an estimate to the area of the boundary of Miao-Tam critical metrics on compact three-manifolds. In addition, we obtain a Bochner type formula which enables us to show that a Miao-Tam critical metric on a compact three-manifold with positive scalar curvature must be isometric to a geodesic ball in $Bbb{S}^3.$



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