TY - JOUR
T1 - Stability of Capillary Hypersurfaces with Planar Boundaries
AU - Li, Haizhong
AU - Xiong, Changwei
N1 - Publisher Copyright:
© 2016, Mathematica Josephina, Inc.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - We prove that, in a Euclidean domain bounded by hyperplanes having linearly independent normals, a connected oriented compact immersed stable capillary hypersurface Mn disjoint from the edges of the domain and with the contact angles belonging to [ π/ 2 , π] must be part of a sphere, if ∂M is embedded for n= 2 , or ∂M is convex in the hyperplane for n≥ 3. By applying a similar argument, we also discuss two other cases where a stable capillary hypersurface must be part of a sphere.
AB - We prove that, in a Euclidean domain bounded by hyperplanes having linearly independent normals, a connected oriented compact immersed stable capillary hypersurface Mn disjoint from the edges of the domain and with the contact angles belonging to [ π/ 2 , π] must be part of a sphere, if ∂M is embedded for n= 2 , or ∂M is convex in the hyperplane for n≥ 3. By applying a similar argument, we also discuss two other cases where a stable capillary hypersurface must be part of a sphere.
KW - Capillary hypersurfaces
KW - Planar boundary
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84952877798&partnerID=8YFLogxK
U2 - 10.1007/s12220-015-9674-7
DO - 10.1007/s12220-015-9674-7
M3 - Article
SN - 1050-6926
VL - 27
SP - 79
EP - 94
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 1
ER -