2022/11/13 by Ma, Hui, Qian, Chao, Wu, Jing +1
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2211.06836
Let G be a compact connected subgroup of SO(n+1). In ℝn+1, we gain interior G-symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (CMC) which have G-invariant boundaries and G-invariant contact angles along boundaries. The main ingredients of the proof are to build an associated Cauchy problem based on infinitesimal Lie group actions, and to apply Morrey's regularity theory and the Cauchy-Kovalevskaya Theorem. Moreover, we also investigate the same kind of symmetry inheritance from boundaries for hypersurfaces of constant higher order mean curvature and Helfrich-type hypersurfaces in ℝn+1.