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arXiv · 2608.28793

On the complete maximal maps and their singularities

Rivu Bardhan·Indranil Biswas·Pradip Kumar·Subham Paul
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Abstract

This article investigates the global structure of maximal surfaces (space-like immersions with zero mean curvature) in Lorentz-Minkowski $3$-space $\mathbb{E}^3_1$, especially focusing on the interplay between genus, the number of singular components--loci, and simple ends. We construct complete maximal maps with arbitrarily many singular components for any genus $p\geq 0$ with simple ends.

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Rivu Bardhan, Indranil Biswas, Pradip Kumar, Subham Paul. 2026-08-28. On the complete maximal maps and their singularities. https://arxiv.org/abs/2608.28793

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