A Prescribed Scalar and Boundary Mean Curvature Problem and the Yamabe Classification on Asymptotically Euclidean Manifolds with Inner Boundary

被引:1
作者
Sicca, Vladmir [1 ]
Tsogtgerel, Gantumur [1 ]
机构
[1] McGill Univ, Montreal, PQ, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
Prescribed curvature problem; Yamabe problem; Asymptotically Euclidean manifolds; Geometric analysis; Differential geometry; Conformal geometry; EINSTEIN CONSTRAINT EQUATIONS;
D O I
10.1007/s12220-023-01346-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the problem of finding a metric in a given conformal class with prescribed non-positive scalar curvature and non-positive boundary mean curvature on an asymptotically Euclidean manifold with inner boundary. We obtain a necessary and sufficient condition in terms of a conformal invariant of the zero sets of the target curvatures for the existence of solutions to the problem and use this result to establish the Yamabe classification of metrics in those manifolds with respect to the solvability of the prescribed curvature problem.
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页数:32
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