Maxfaces with infinitely many Swallowtails

Fuente: arXiv
Saved in:
Bibliographic Details
Main Author: Dhochak, Anu
Format: Preprint
Published: 2026
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910146328788992
author Dhochak, Anu
author_facet Dhochak, Anu
contents 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 $n=2$, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_17520
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Maxfaces with infinitely many Swallowtails
Dhochak, Anu
Differential Geometry
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 $n=2$, 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.
title Maxfaces with infinitely many Swallowtails
topic Differential Geometry
url https://arxiv.org/abs/2604.17520