In this paper, we consider the alpha-Gauss curvature flow for complete convex graphs over horosphere in the hyperbolic space. We show that for all positive power alpha > 0, if the initial hypersurface is smooth, complete non-compact uniformly convex graph over R(n )and bounded by two horospheres, then the solution of the flow exists for all time. Moreover, the evolution of horospheres act as barriers along the flow.
Evolution of graphs in hyperbolic space by their Gauss curvature
Pan, ShujingFirst
;
2024-01-01
Abstract
In this paper, we consider the alpha-Gauss curvature flow for complete convex graphs over horosphere in the hyperbolic space. We show that for all positive power alpha > 0, if the initial hypersurface is smooth, complete non-compact uniformly convex graph over R(n )and bounded by two horospheres, then the solution of the flow exists for all time. Moreover, the evolution of horospheres act as barriers along the flow.
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