Lipschitz Continuous Hypersurfaces with Prescribed Curvature and Asymptotic Boundary in Hyperbolic Space
Zhenan Sui, Wei Sun
TL;DR
This paper proves the existence of a complete hypersurface in hyperbolic space that has a specified curvature and boundary at infinity, using Lipschitz continuity in a weak sense.
Contribution
It establishes the existence of Lipschitz continuous hypersurfaces with prescribed curvature and boundary at infinity in hyperbolic space, under certain conditions.
Findings
Existence of such hypersurfaces is proven.
Hypersurfaces have prescribed Weingarten curvature.
Hypersurfaces have prescribed asymptotic boundary.
Abstract
We prove the existence of a complete locally Lipschitz continuous hypersurface in weak sense with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under certain assumptions.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering