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

Yujie Wu

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arXiv · 2405.03993

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

Yujie Wu

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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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BibTeX RIS

Yujie Wu. 2024-05-07. Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary. https://arxiv.org/abs/2405.03993

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