Discrete constant mean curvature surfaces on general graphs-Reference-Cited by-同舟云学术

Discrete constant mean curvature surfaces on general graphs

Published:2022-09-29 Issue:6 Volume:216 Page:
ISSN:0046-5755
Container-title:Geometriae Dedicata
language:en
Short-container-title:Geom Dedicata

Author:

Hoffmann Tim,Kobayashi Shimpei,Ye Zi^ORCID

Abstract

AbstractThe contribution of this paper is twofold. First, we generalize the definition of discrete isothermic surfaces. Compared with the previous ones, it covers more discrete surfaces, e.g., the associated families of discrete isothermic minimal and non-zero constant mean curvature (CMC in short) surfaces, whose counterpart in smooth case are isothermic surfaces. Second, we show that the discrete isothermic CMC surfaces can be obtained by the discrete holomorphic data (a solution of the additive rational Toda system) via the discrete generalized Weierstrass type representation.

Funder

Deutsche Forschungsgemeinschaft

Publisher

Springer Science and Business Media LLC

Subject

Geometry and Topology

Link

https://link.springer.com/content/pdf/10.1007/s10711-022-00733-3.pdf

Reference15 articles.

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3. Bobenko, A., Romon, P.: Discrete CMC surfaces in $$\mathbb{R} ^3$$ and discrete minimal surfaces in $$\mathbb{S}^3$$ : a discrete Lawson correspondence. J. Integ. Syst. 2(1), 18 (2017)

4. Bobenko, A., Suris, Y.: Integrable systems on quad-graphs. Int. Math. Res. Not. 2002(11), 573–611 (2002)

5. Dorfmeister, J., Pedit, F., Hongyong, W.: Weierstrass type representation of harmonic maps into symmetric spaces. Commun. Anal. Geom. 6(4), 633–668 (1998)

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