Navigating the Space of Symmetric CMC Surfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Lynn Heller
  • Sebastian Heller
  • Nicholas Schmitt

Organisationseinheiten

Externe Organisationen

  • Universität Hamburg
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)413-455
Seitenumfang43
FachzeitschriftJournal of Differential Geometry
Jahrgang110
Ausgabenummer3
PublikationsstatusVeröffentlicht - Nov. 2018

Abstract

In this paper we introduce a flow on the spectral data for symmetric CMC surfaces in the \(3\)-sphere. The flow is designed in such a way that it changes the topology but fixes the intrinsic (metric) and certain extrinsic (periods) closing conditions of the CMC surfaces. For rational times we obtain closed (possibly branched) connected CMC surfaces of higher genus. We prove the short time existence of this flow near the spectral data of (a class of) CMC tori. In particular we prove that flowing the spectral data for the Clifford torus is equivalent to the flow of Plateau solutions by varying the angle of the fundamental piece in Lawson's construction for the minimal surfaces \(\xi_{g,1}.\)

ASJC Scopus Sachgebiete

Zitieren

Navigating the Space of Symmetric CMC Surfaces. / Heller, Lynn; Heller, Sebastian; Schmitt, Nicholas.
in: Journal of Differential Geometry, Jahrgang 110, Nr. 3, 11.2018, S. 413-455.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Heller, L, Heller, S & Schmitt, N 2018, 'Navigating the Space of Symmetric CMC Surfaces', Journal of Differential Geometry, Jg. 110, Nr. 3, S. 413-455. https://doi.org/10.48550/arXiv.1501.01929, https://doi.org/10.4310/jdg/1542423626
Heller, L., Heller, S., & Schmitt, N. (2018). Navigating the Space of Symmetric CMC Surfaces. Journal of Differential Geometry, 110(3), 413-455. https://doi.org/10.48550/arXiv.1501.01929, https://doi.org/10.4310/jdg/1542423626
Heller L, Heller S, Schmitt N. Navigating the Space of Symmetric CMC Surfaces. Journal of Differential Geometry. 2018 Nov;110(3):413-455. doi: 10.48550/arXiv.1501.01929, 10.4310/jdg/1542423626
Heller, Lynn ; Heller, Sebastian ; Schmitt, Nicholas. / Navigating the Space of Symmetric CMC Surfaces. in: Journal of Differential Geometry. 2018 ; Jahrgang 110, Nr. 3. S. 413-455.
Download
@article{50e2831a3a5f4df1b7bc005bcff28f38,
title = "Navigating the Space of Symmetric CMC Surfaces",
abstract = " In this paper we introduce a flow on the spectral data for symmetric CMC surfaces in the \(3\)-sphere. The flow is designed in such a way that it changes the topology but fixes the intrinsic (metric) and certain extrinsic (periods) closing conditions of the CMC surfaces. For rational times we obtain closed (possibly branched) connected CMC surfaces of higher genus. We prove the short time existence of this flow near the spectral data of (a class of) CMC tori. In particular we prove that flowing the spectral data for the Clifford torus is equivalent to the flow of Plateau solutions by varying the angle of the fundamental piece in Lawson's construction for the minimal surfaces \(\xi_{g,1}.\) ",
keywords = "math.DG, 53A10, 53C42, 53C43",
author = "Lynn Heller and Sebastian Heller and Nicholas Schmitt",
note = "Funding information: Acknowledgment. We would like to thank the anonymous referee for his helpful comments which enabled us to improve the presentation of the paper. The first author is supported by the European Social Fund and by the Ministry of Science, Research and the Arts Baden– W{\"u}rtemberg, the other authors are supported by the DFG through the project HE 6829/1-1.",
year = "2018",
month = nov,
doi = "10.48550/arXiv.1501.01929",
language = "English",
volume = "110",
pages = "413--455",
number = "3",

}

Download

TY - JOUR

T1 - Navigating the Space of Symmetric CMC Surfaces

AU - Heller, Lynn

AU - Heller, Sebastian

AU - Schmitt, Nicholas

N1 - Funding information: Acknowledgment. We would like to thank the anonymous referee for his helpful comments which enabled us to improve the presentation of the paper. The first author is supported by the European Social Fund and by the Ministry of Science, Research and the Arts Baden– Würtemberg, the other authors are supported by the DFG through the project HE 6829/1-1.

PY - 2018/11

Y1 - 2018/11

N2 - In this paper we introduce a flow on the spectral data for symmetric CMC surfaces in the \(3\)-sphere. The flow is designed in such a way that it changes the topology but fixes the intrinsic (metric) and certain extrinsic (periods) closing conditions of the CMC surfaces. For rational times we obtain closed (possibly branched) connected CMC surfaces of higher genus. We prove the short time existence of this flow near the spectral data of (a class of) CMC tori. In particular we prove that flowing the spectral data for the Clifford torus is equivalent to the flow of Plateau solutions by varying the angle of the fundamental piece in Lawson's construction for the minimal surfaces \(\xi_{g,1}.\)

AB - In this paper we introduce a flow on the spectral data for symmetric CMC surfaces in the \(3\)-sphere. The flow is designed in such a way that it changes the topology but fixes the intrinsic (metric) and certain extrinsic (periods) closing conditions of the CMC surfaces. For rational times we obtain closed (possibly branched) connected CMC surfaces of higher genus. We prove the short time existence of this flow near the spectral data of (a class of) CMC tori. In particular we prove that flowing the spectral data for the Clifford torus is equivalent to the flow of Plateau solutions by varying the angle of the fundamental piece in Lawson's construction for the minimal surfaces \(\xi_{g,1}.\)

KW - math.DG

KW - 53A10, 53C42, 53C43

UR - http://www.scopus.com/inward/record.url?scp=85057039251&partnerID=8YFLogxK

U2 - 10.48550/arXiv.1501.01929

DO - 10.48550/arXiv.1501.01929

M3 - Article

VL - 110

SP - 413

EP - 455

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 3

ER -