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On the Positive Mass Theorem for Closed Riemannian Manifolds

In: From Riemann to Differential Geometry and Relativity

Author

Listed:
  • Andreas Hermann

    (Institut für Mathematik, Universität Potsdam)

  • Emmanuel Humbert

    (LMPT, Université de Tours)

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.

Suggested Citation

  • Andreas Hermann & Emmanuel Humbert, 2017. "On the Positive Mass Theorem for Closed Riemannian Manifolds," Springer Books, in: Lizhen Ji & Athanase Papadopoulos & Sumio Yamada (ed.), From Riemann to Differential Geometry and Relativity, pages 515-540, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60039-0_17
    DOI: 10.1007/978-3-319-60039-0_17
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