TY - JOUR
T1 - Characterizations of Umbilical Hypersurfaces by Partially Overdetermined Problems in Space Forms
AU - Xie , Yangsen
JO - Journal of Mathematical Study
VL - 3
SP - 286
EP - 313
PY - 2025
DA - 2025/09
SN - 58
DO - http://doi.org/10.4208/jms.v58n3.25.03
UR - https://global-sci.org/intro/article_detail/jms/24409.html
KW - Rigidity, umbilical hypersurfaces, Serrin’s overdetermined problem, space forms,
contact angle.
AB - <p style="text-align: justify;">In this paper, we characterize the rigidity of umbilical hypersurfaces by a
Serrin-type partially overdetermined problem in space forms, which generalizes the
similar results in Euclidean half-space and Euclidean half-ball. Guo-Xia first obtained
these rigidity results when the Robin boundary condition on the support hypersurface
is homogeneous, at this time the target umbilical hypersurface has orthogonal contact
angle 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.</p>