Zero mean curvature surfaces in Lorentz-Minkowski 3-space which change type across a light-like line

TL;DR

This paper constructs the first known examples of zero mean curvature surfaces in Lorentz-Minkowski 3-space that change type across a light-like line, expanding understanding of singularities in such surfaces.

Contribution

It provides the first explicit examples of zero mean curvature surfaces changing type across a light-like line, extending previous work and generalizing to higher dimensions.

Findings

First examples of such surfaces with light-like line singularities

Surfaces change type across the light-like line

Extension to higher-dimensional zero mean curvature hypersurfaces

Abstract

It is well-known that space-like maximal surfaces and time-like minimal surfaces in Lorentz-Minkowski 3-space R^3_1 have singularities in general. They are both characterized as zero mean curvature surfaces. We are interested in the case where the singular set consists of a light-like line, since this case has not been analyzed before. As a continuation of a previous work by the authors, we give the first example of a family of such surfaces which change type across the light-like line. As a corollary, we also obtain a family of zero mean curvature hypersurfaces in R^{n+1}_1 that change type across an (n-1)-dimensional light-like plane.