Details
| Original language | English |
|---|---|
| Pages (from-to) | 413-455 |
| Number of pages | 43 |
| Journal | Journal of Differential Geometry |
| Volume | 110 |
| Issue number | 3 |
| Publication status | Published - Nov 2018 |
Abstract
Keywords
- math.DG, 53A10, 53C42, 53C43
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Algebra and Number Theory
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In: Journal of Differential Geometry, Vol. 110, No. 3, 11.2018, p. 413-455.
Research output: Contribution to journal › Article › Research › peer review
}
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 -