PreprintCC BY 4.0arXiv
On the complete maximal maps and their singularities
Abstract
This article investigates the global structure of maximal surfaces (space-like immersions with zero mean curvature) in Lorentz-Minkowski $3$-space 𝔼31, 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≥ 0 with simple ends.
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BibTeX
@misc{bardhan2026complete,
title = {{On the complete maximal maps and their singularities}},
author = {Rivu Bardhan and Indranil Biswas and Pradip Kumar and Subham Paul},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28793},
eprint = {2608.28793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28793},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the complete maximal maps and their singularities
AU - Rivu Bardhan
AU - Indranil Biswas
AU - Pradip Kumar
AU - Subham Paul
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2608.28793
UR - https://arxiv.org/abs/2608.28793
AB - This article investigates the global structure of maximal surfaces (space-like immersions with zero mean curvature) in Lorentz-Minkowski $3$-space 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≥ 0 with simple ends.
ER -