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Yujie Wu, Capillary Surfaces in Manifolds with Nonnegative Scalar Curvature and Strictly Mean Convex Boundary, International Mathematics Research Notices, Volume 2025, Issue 9, May 2025, rnaf106, https://doi.org/10.1093/imrn/rnaf106
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Abstract
In this paper we use generalized 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 surfaces 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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