Rigidity Theorems for Compact Manifolds with Boundary and Positive Ricci Curvature
By Fengbo Hang, Xiaodong Wang. 2009
60 citations recorded by the source corpus.
We prove some boundary rigidity results for the hemisphere under a lower bound for Ricci curvature. The main result can be viewed as the Ricci version of a conjecture of Min-Oo.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/017548f563f6b3de1d2e65a093fb3e619a843dba
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Rigidity of min-max minimal spheres in three-manifolds (2011, background): “al sphere Σ, of index zero or one, with |Σ| <4π. Remark. Toponogov [37] proved that the length of any simple closed geodesic contained in a two-sphere with scalar curvature R≥ 2 is at most 2π. See [17] for a different proof. It is not difficult to see that there is no such bound for the area of a mi”
- Rigidity of Area-Minimizing Hyperbolic Surfaces in Three-Manifolds (2011, background): “We refer the reader to [14, 10, 16] for partial results concerning the Min-Oo’s conjecture.”
- Rigidity of area-minimizing two-spheres in three-manifolds (2010, background): “Moreover, equality holds if and only if (Σ, g) is isometric to the standard sphere S2 up to scaling (see also [7] for a different proof).”
- On static three-manifolds with positive scalar curvature (2015, methodology): “ 4 LUCAS AMBROZIO [17]. In view of that, Theorem 2 gives an interesting rigidity result for the standard round hemisphere under a nice extra geometric assumption (for related results, see for example [32], [22] and [42]). In this paper we prove some classification results for static three-manifolds w”