Maximal hypersurfaces with prescribed light-like cones in Lorentz-Minkowski space
Huyuan Chen, Ying Wang, Feng Zhou
TL;DR
This paper investigates maximal hypersurfaces in Lorentz-Minkowski space with prescribed light-like cones, constructing weak solutions to the mean curvature equation with multiple Dirac masses through an approximation method.
Contribution
It introduces a novel approach to construct weak solutions for maximal hypersurfaces with multiple light-cones using approximation techniques.
Findings
Constructed weak solutions via approximation with smooth sources.
Extended the understanding of maximal hypersurfaces with prescribed light-like cones.
Provided a framework for handling multiple Dirac masses in Lorentz-Minkowski space.
Abstract
The purpose in this paper is to study the maximal hypersurfaces with multiple light-cones in Lorentz-Minkowski space by considering the weak solutions to the mean curvature equation with multiple Dirac masses. Such solutions are constructed via an approximation procedure, using regular solutions with smooth sources that converge weakly to the Dirac measures.
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