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

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**137**(2009), 2733-2740 Request permission

## Abstract:

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 M. Min-Oo’s on the scalar curvature rigidity of the upper hemisphere.## References

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## Additional Information

**Michael Eichmair**- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
- Email: eichmair@math.mit.edu
- Received by editor(s): December 3, 2007
- Received by editor(s) in revised form: September 17, 2008
- Published electronically: April 3, 2009
- Communicated by: Richard A. Wentworth
- © Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 2733-2740 - MSC (2000): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-09-09789-5
- MathSciNet review: 2497486