Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas

TL;DR

This paper constructs new examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space using Konderak's formulas, revealing a richer variety of such surfaces than previously known.

Contribution

The paper introduces novel entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space, including examples not belonging to Kobayashi surfaces, expanding the known class of such surfaces.

Findings

Existence of entire zero-mean curvature graphs over space-like planes

Existence of entire zero-mean curvature graphs over light-like planes

These graphs form a large and interesting class of surfaces in Lorentz-Minkowski space

Abstract

Using Konderak's representation formula, we construct an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski 3-space over a space-like plane, which does not belong to the class of "Kobayashi surfaces". We also point out the existence of an entire zero-mean curvature graph of mixed-type in Lorentz-Minkowski space over a light-like plane. These examples suggest that entire mixed-type zero-mean curvature graphs contain an unexpectedly large number of interesting examples.