Maxfaces with infinitely many Swallowtails
Differential Geometry
2026-04-21 v1
Abstract
In this article, we discuss the existence of a 1-parameter infinite genus family of maxfaces having infinitely many planar (spacelike) ends and infinitely many swallowtails. In particular, we show the existence of the following: (1) a period-2 family of maxfaces with infinitely many planar ends and alternating singularity types, where every odd-layer neck has exactly four swallowtails, while each even-layer neck is almost conical; for , the fundamental piece is a genus-1 Wei-type maxface; (2) a period-3 family where every neck carries four swallowtails (24 per period); and (3) a period-2 family of maxfaces with an almost conical singularity on every neck. All maxfaces are embedded in a wider sense.
Cite
@article{arxiv.2604.17520,
title = {Maxfaces with infinitely many Swallowtails},
author = {Anu Dhochak},
journal= {arXiv preprint arXiv:2604.17520},
year = {2026}
}