On the Positive Mass Theorem for Closed Riemannian Manifolds

Andreas Hermann () and Emmanuel Humbert ()
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Andreas Hermann: Institut für Mathematik, Universität Potsdam
Emmanuel Humbert: LMPT, Université de Tours

A chapter in From Riemann to Differential Geometry and Relativity, 2017, pp 515-540 from Springer

Abstract: Abstract The Positive Mass Conjecture for asymptotically flat Riemannian manifolds is a famous open problem in geometric analysis. In this article we consider a variant of this conjecture, namely the Positive Mass Conjecture for closed Riemannian manifolds. We explain why the two positive mass conjectures are equivalent. After that we explain our proof of the following result: If one can prove the Positive Mass Conjecture for one closed simply-connected non-spin manifold of dimension n $$\ge $$ 5 then the Positive Mass Conjecture is true for all closed manifolds of dimension n.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60039-0_17

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DOI: 10.1007/978-3-319-60039-0_17

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