Rigidity of Area-Minimizing Free Boundary Surfaces in Mean Convex Three-Manifolds
By L. Ambrozio. 2013
73 citations recorded by the source corpus.
We prove a local splitting theorem for three-manifolds with mean convex boundary and scalar curvature bounded from below that contain certain locally area-minimizing free boundary surfaces. Our methods are based on those of Micallef and Moraru (Splitting of 3-manifolds and rigidity of area-minimizing surfaces, arXiv:1107.5346, 2011). We use this local result to establish a global rigidity theorem for area-minimizing free boundary disks. In the negative scalar curvature case, this global result implies a rigidity theorem for solutions of the Plateau problem with length-minimizing boundary.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/0b13f855adc13c456362865f927d59f08fb16195
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Compactness analysis for free boundary minimal hypersurfaces (2017, methodology): “Appendix of [39]) and its differential can be computed using the result of Proposition 17 in [2], so that”