Low index capillary minimal surfaces in Riemannian 3-manifolds (Q2117491)

In this work, the author prove a local rigidity result for infinitesimally rigid capillary surfaces in some Riemannian 3-manifolds with mean-convex boundary. After that the author 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.