Navigating the space of symmetric CMC surfaces

Autor: Nicholas Schmitt, Sebastian Heller, Lynn Heller
Rok vydání: 2018
Předmět:
Zdroj: J. Differential Geom. 110, no. 3 (2018), 413-455
ISSN: 0022-040X
DOI: 10.4310/jdg/1542423626
Popis: 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 $\xi_{g,1}.$
Comment: 43 pages, 4 figures, accepted for publication in J. Differential Geo
Databáze: OpenAIRE