Discrete surfaces of constant mean curvature

Abstract

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.

Cited by in corpus (6)

• Discrete linear Weingarten surfaces
• Semi-discrete isothermic surfaces
• Discrete constant mean curvature nets in space forms: Steiner's formula and Christoffel duality
• Discrete cyclic systems and circle congruences
• Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms
• Discrete constant mean curvature surfaces via conserved quantities