The size of isoperimetric surfaces in 3-manifolds and a rigidity result for the upper hemisphere

Details The size of isoperimetric surfaces in 3-manifolds and a rigidity result for the upper hemisphere The size of isoperimetric surfaces in 3-manifolds and a rigidity result for the upper hemisphere

2007-06-24

arxiv.org/abs/0706.3483v4

Mathematics

Differential Geometry

9 pages. Thoroughly revised final version. Comments welcome!

Scientific paper

We characterize the standard $\mathbb{S}^3$ as the closed Ricci-positive
3-manifold with scalar curvature at least 6 having isoperimetric surfaces of
largest area: $4\pi$. As a corollary we answer in the affirmative an
interesting special case of a conjecture of Min-Oo's on the scalar curvature
rigidity of the upper hemisphere..

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