Deformations of the hemisphere that increase scalar curvature

Simon Brendle, Fernando C. Marques, Andre Neves

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

Consider a compact Riemannian manifold M of dimension n whose boundary ∂M is totally geodesic and is isometric to the standard sphere Sn-1. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere Sn+ equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's Conjecture in dimension n≥3.

Original languageEnglish (US)
Pages (from-to)175-197
Number of pages23
JournalInventiones Mathematicae
Volume185
Issue number1
DOIs
StatePublished - Jul 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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