Characterizations of Umbilical Hypersurfaces by Partially Overdetermined Problems in Space Forms (Journal of Mathematical Study, 2025)
In this paper, we characterize the rigidity of umbilical hypersurfaces by aSerrin-type partially overdetermined problem in space forms, which generalizes thesimilar results in Euclidean half-space and Euclidean half-ball. Guo-Xia first obtainedthese rigidity results when the Robin boundary condition on the support hypersurfaceis homogeneous, at this time the target umbilical hypersurface has orthogonal contactangle with the support. However, in this paper we can obtain any contact angle $θ ∈(0,π)$ by changing the Robin boundary condition to be inhomogeneous.