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arXiv · 2605.06409

Entire spacelike radial graphs with prescribed mean curvature in the Lorentz--Minkowski space

Gabriele Cora·Alessandro Iacopetti·Lorenzo Maniscalco
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Abstract

In this paper we address the existence and uniqueness of entire spacelike hypersurfaces in the Lorentz--Minkowski space $\mathbb{L}^{m+1}$ with prescribed mean curvature that are star-shaped with respect to a point and asymptotic to a light cone. We also establish a Willmore-type inequality and prove a non-existence result for spacelike radial graphs asymptotic to the light cone whose mean curvature belongs to $L^p$ for $1 \leq p\leq m$, in particular in the case of compactly supported mean curvature.

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Gabriele Cora, Alessandro Iacopetti, Lorenzo Maniscalco. 2026-05-07. Entire spacelike radial graphs with prescribed mean curvature in the Lorentz--Minkowski space. https://arxiv.org/abs/2605.06409

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