Curvature estimates for spacelike graphic hypersurfaces in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$

Abstract

In this paper, we can obtain curvature estimates for spacelike admissible graphic hypersurfaces in the $(n+1)$-dimensional Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$, and through which the existence of spacelike admissible graphic hypersurfaces, with prescribed $2$-th Weingarten curvature and Dirichlet boundary data, defined over a strictly convex domain in the hyperbolic plane ${\mathcal{H}}^n(1)\subset {\mathbb{R}}_1^{n+1}$ of center at origin and radius $1$, can be proven.

19 pages. Comments are welcome

References in corpus (5)

• A stability result for translating space-like graphs in Lorentz manifolds
• Inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
• An anisotropic inverse mean curvature flow for spacelike graphic hypersurfaces with boundary in Lorentz-Minkowski space ${\mathbb{R}}_1^{n+1}$
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