Communications in Analysis and Geometry

Volume 24 (2016)

Number 4

A positive mass theorem for asymptotically flat manifolds with a non-compact boundary

Pages: 673 – 715

DOI: http://dx.doi.org/10.4310/CAG.2016.v24.n4.a1

Authors

Sérgio Almaraz (Instituto de Matemática, Universidade Federal Fluminense (UFF), Niterói, RJ, Brazil)

Ezequiel Barbosa (Departamento de Matemática, Universidade Federal de Minas Gerais (UFMG), Belo Horizonte, MG, Brazil)

Levi Lopes de Lima (Departamento de Matemática, Universidade Federal do Ceará (UFC), Fortaleza, CE, Brazil)

Abstract

We define a mass-type invariant for $n$-dimensional asymptotically flat manifolds with a non-compact boundary and prove a positive mass theorem if either $3 \leq n \leq 7$ or if $n \geq 3$ and the manifold is spin. This settles, for this class of manifolds, a question posed in a recent paper by the first author in connection with the longterm behavior of a certain Yamabe-type flow on scalar-flat compact manifolds with boundary.

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