Emma Carberry

The closure of spectral data for constant mean curvature tori in 𝕊³

Publisher: Walter de Gruyter GmbH

Date: 31-08-2014

DOI: 10.1515/CRELLE-2014-0068

Abstract: The spectral curve correspondence for finite-type solutions of the sinh- Gordon equation describes how they arise from and give rise to hyperelliptic curves with a real structure. Constant mean curvature (CMC) 2-tori in 𝕊 3 ${\\mathbb{S}^{3}}$ result when these spectral curves satisfy periodicity conditions. We prove that the spectral curves of CMC tori are dense in the space of smooth spectral curves of finite-type solutions of the sinh-Gordon equation. One consequence of this is the existence of countably many real n -dimensional families of CMC tori in 𝕊 3 ${\\mathbb{S}^{3}}$ for each positive integer n .

Harmonic Maps and Integrable Systems

Publisher: American Mathematical Society

Date: 2013

DOI: 10.1090/CONM/597/11770

The prevalence of tori amongst constant mean curvature planes in

Publisher: Elsevier BV

Date: 08-2016

DOI: 10.1016/J.GEOMPHYS.2016.04.010

Whitham deformations and the space of harmonic tori in S3

Publisher: Wiley

Date: 23-12-2018

DOI: 10.1112/JLMS.12191

Darboux transforms and spectral curves of constant mean curvature surfaces revisited

Publisher: Springer Science and Business Media LLC

Date: 09-08-2012

DOI: 10.1007/S10455-012-9347-8

The space of equivariant harmonic tori in the 3-sphere

Publisher: Elsevier BV

Date: 11-2020

DOI: 10.1016/J.GEOMPHYS.2020.103808

Mininal tori in S³

Publisher: Mathematical Sciences Publishers

Date: 11-2007

DOI: 10.2140/PJM.2007.233.41

Harmonic tori in De Sitter spaces S²ⁿ1

Publisher: Springer Science and Business Media LLC

Date: 09-06-2014

DOI: 10.1007/S10711-013-9873-Y

Toda frames, harmonic maps and extended Dynkin diagrams

Publisher: Elsevier BV

Date: 06-2017

DOI: 10.1016/J.DIFGEO.2017.03.011

University Of Sydney

Location: Australia

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Princeton University

Location: United States of America

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Monash University

Location: Australia

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Brown Fellowship

Start Date: 2017

End Date: 2017

Funder: University of Sydney