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SPHERICAL CAPS IN A CONVEX CONE
Taekwan Um 충청수학회 2013 충청수학회지 Vol.26 No.3
We show that a compact embedded hypersurface with ratio of mean curvature functions in a convex cone C ½ Rn+1 is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to @C:
SPHERICAL CAPS IN A CONVEX CONE
Um, Taekwan Chungcheong Mathematical Society 2013 충청수학회지 Vol.26 No.3
We show that a compact embedded hypersurface with constant ratio of mean curvature functions in a convex cone $C{\subset}\mathbb{R}^{n+1}$ is part of a hypersphere if it has a point where all the principal curvatures are positive and if it is perpendicular to ${\partial}C$.