Cambridge Journal of Mathematics

Volume 10 (2022)

Number 4

Free boundary minimal surfaces with connected boundary and arbitrary genus

Pages: 835 – 857

DOI: https://dx.doi.org/10.4310/CJM.2022.v10.n4.a3

Authors

Alessandro Carlotto (Department of Mathematics, Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland)

Giada Franz (Department of Mathematics, Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland)

Mario B. Schulz (Westfälische Wilhelms-Universität (WWU) Münster, Germany)

Abstract

We employ min-max techniques to show that the unit ball in $\mathbb{R}^3$ contains embedded free boundary minimal surfaces with connected boundary and arbitrary genus.

Keywords

minimal surfaces, equivariant min-max theory

2010 Mathematics Subject Classification

Primary 53A10. Secondary 49Q05, 58E12.

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The authors would like to express their gratitude to Ailana Fraser and Brian White for several enlightening conversations at the early stages of this project. This article was completed while A. C. was a visiting scholar at the Institut Mittag-Leffler: the excellent working conditions and the support of the Royal Swedish Academy of Sciences are gratefully acknowledged. The research of M. S. was funded by the EPSRC grant EP/S012907/1.

Received 8 July 2021

Published 21 October 2022