Discrete surfaces of constant mean curvature. arXiv:0804.2707
Preprint, arXiv:0804.2707 [math.DG] (2008).
Summary: We propose a unified definition for discrete analogues of constant mean curvature surfaces in spaces of constant curvature as a special case of discrete special isothermic nets. Bäcklund transformations and Lawson’s correspondence are discussed. It is shown that the definition generalizes previous definitions and a construction for discrete cmc surfaces of revolution in space forms is provided.
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
| 53A30 | Conformal differential geometry (MSC2010) |
| 52C26 | Circle packings and discrete conformal geometry |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K25 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry |
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