# Discrete surfaces of constant mean curvature

@article{Burstall2008DiscreteSO, title={Discrete surfaces of constant mean curvature}, author={Francis Burstall and Udo Hertrich-Jeromin and Wayne Rossman and Susana D. Santos}, journal={arXiv: Differential Geometry}, year={2008} }

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. B\"acklund 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.

## 23 Citations

### Discrete constant mean curvature surfaces via conserved quantities

- Mathematics
- 2010

This survey article is about discrete constant mean curvature surfaces defined by an approach related to integrable systems techniques. We introduce the notion of discrete constant mean curvature…

### Construction of discrete constant mean curvature surfaces in Riemannian spaceforms and applications

- Mathematics
- 2017

### Discrete constant mean curvature nets in space forms: Steiner’s formula and Christoffel duality

- MathematicsDiscret. Comput. Geom.
- 2014

We show that the discrete principal nets in quadrics of constant curvature that have constant mixed area mean curvature can be characterized by the existence of a Königs dual in a concentric quadric.

### ISOTHERMICITY FOR DISCRETE SURFACES IN THE EUCLIDEAN AND MINKOWSKI 3-SPACES

- Mathematics
- 2010

In this report we explain why a certain notion of isothermicity for discrete surfaces in Euclidean 3-space is natural. We also consider isothermicity of discrete surfaces in Minkowski 3-space.

### Discrete linear Weingarten surfaces

- Mathematics
- 2013

Discrete linear Weingarten surfaces in space forms are characterized as special discrete Ω-nets, a discrete analogue of Demoulin’s Ω-surfaces. It is shown that the Lie-geometric deformation of Ω-nets…

### Weierstrass representation for semi-discrete minimal surfaces

- Mathematics
- 2018

We give a Weierstrass type representation for semi-discrete minimal surfaces in Euclidean 3-space. In this paper, we introduce this result, and another related work about discretized maximal surfaces…

### On Discrete Constant Mean Curvature Surfaces

- MathematicsDiscret. Comput. Geom.
- 2014

This work shows an incidence geometric characterization of a pair of parallel quadrilaterals having a discrete mean curvature value of −1 and establishes a discrete Weierstrass-type representation for discrete cmc surfaces.

### Semi-discrete isothermic surfaces

- Mathematics
- 2015

A Darboux transformation for polarized space curves is introduced and its properties are studied, in particular, Bianchi permutability. Semi-discrete isothermic surfaces are described as sequences of…

### Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms

- Mathematics
- 2016

In this paper we define and analyze singularities of discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms. In particular,…

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