Rigidity of area-minimizing two-spheres in three-manifolds

By H. Bray, S. Brendle, A. Neves. 2010

129 citations recorded by the source corpus.

We give a sharp upper bound for the area of a minimal two-sphere in a three-manifold (M,g) with positive scalar curvature. If equality holds, we show that the universal cover of (M,g) is isometric to a cylinder.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d78b6d91ca615fa420c4af4ee06ec223be61aa76

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Otis Chodosh
2. Antoine Song
3. Ivaldo Nunes
4. Jintian Zhu
5. L. Ambrozio
6. A. Neves

In Geometry and Topology

1. Otis Chodosh
2. Ivaldo Nunes
3. Jintian Zhu
4. Antoine Song
5. L. Ambrozio
6. A. Neves

Citations in the corpus

• Rigidity of Area-Minimizing Hyperbolic Surfaces in Three-Manifolds (2011, methodology): “The same construction was used in [1] and [4] to prove similar rigidity results.”
• Generalized soap bubbles and the topology of manifolds with positive scalar curvature (2020, background): “One intuitive way to approach this would be to exploit the fact that stable minimal surfaces in a three manifold with scalar curvature ≥ 2 are spherical and have area ≤ 4π (see [2] for a related rigidity result).”
• Existence of infinitely many minimal hypersurfaces in closed manifolds (2018, background): “I also thank him for pointing out references [39] and [5].”
• Width estimate and doubly warped product (2020, background): “Once this is done, the rigidity result comes from a standard foliation argument from [1] (see also [9]).”