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arXiv · 2505.21869

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

Takeki Komatsu·Masaaki Umehara
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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.

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Takeki Komatsu, Masaaki Umehara. 2025-05-28. Examples of entire zero-mean curvature graphs of mixed-type in Lorentz-Minkowski space via Konderak's formulas. https://arxiv.org/abs/2505.21869

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