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arXiv · 1301.6257

Rigidity of area-minimizing free boundary surfaces in mean convex three-manifolds

Lucas C. Ambrozio
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Abstract

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. 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.

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Lucas C. Ambrozio. 2013-01-26. Rigidity of area-minimizing free boundary surfaces in mean convex three-manifolds. https://arxiv.org/abs/1301.6257

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