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Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary

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arxiv 2405.03993 v2 pith:FTXQ7VRG submitted 2024-05-07 math.DG

Yujie Wu This is my paper
classification math.DG
keywords manifoldsboundarycapillaryconvexcurvaturemeannonnegativescalar
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abstract

In this paper we use stable capillary surfaces (analogous to the $\mu$-bubble construction) to study manifolds with strictly mean convex boundary and nonnegative scalar curvature. We give an obstruction to filling 2-manifolds by such 3-manifolds based on the Urysohn width. We also obtain a bandwidth estimate and establish other geometric properties of such manifolds.

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Cited by 1 Pith paper

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  1. Geometric Stability of the Schoen-Yau Zero Mass Theorem

    math.DG 2026-04 unverdicted novelty 2.0 of 10

    The paper reviews progress on geometric stability of the zero ADM mass rigidity theorem and states that it remains an open question which notion of geometric convergence best captures this stability even in three dimensions.

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