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Low index capillary minimal surfaces in Riemannian $3$-manifolds
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math.DG
keywords
boundarycapillaryindexmanifoldsminimalriemanniansurfacesambient
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abstract
We prove a local rigidity result for infinitesimally rigid capillary surfaces in some Riemannian $3$-manifolds with mean convex boundary. We also derive bounds on the genus, number of boundary components and area of any compact two-sided capillary minimal surface with low index under certain assumptions on the curvature of the ambient manifold and of its boundary.
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