TY - JOUR
T1 - Deformations of the hemisphere that increase scalar curvature
AU - Brendle, Simon
AU - Marques, Fernando C.
AU - Neves, Andre
N1 - Funding Information:
The first author was supported in part by the National Science Foundation under grant DMS-0905628. The second author was supported by CNPq-Brazil, FAPERJ, and the Stanford Department of Mathematics.
PY - 2011/7
Y1 - 2011/7
N2 - 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.
AB - 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.
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U2 - 10.1007/s00222-010-0305-4
DO - 10.1007/s00222-010-0305-4
M3 - Article
AN - SCOPUS:79958862624
SN - 0020-9910
VL - 185
SP - 175
EP - 197
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -