# Discrete Parametrized Surface Theory in $\mathbb{R}^3$

Tim Hoffmann, Andrew O'Shea Sageman-Furnas, Max Wardetzky

### Description

A discrete surface theory in $\mathbb{R}^3$ that unites the most prevalent versions of discrete special parametrizations is introduced here. The theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. Our theory is not restricted to integrable geometries, but extends to a general surface theory.

### References

• Tim Hoffmann, Andrew O. Sageman-Furnas, and Max Wardetzky.
A Discrete Parametrized Surface Theory in $\mathbb R^3$.
International Mathematics Research Notices, 2017(14):4217–4258, 2017.
arXiv:1412.7293, doi:10.1093/imrn/rnw015.

#### Prof. Dr. Tim Hoffmann   +

Projects: A02
University: TU München, Department of Mathematics, 02.06.021
Address: Boltzmannstr. 3, 85748 Garching, GERMANY
Tel: +49 89 28918384
E-Mail: tim.hoffmann[at]ma.tum.de
Website: https://geo.ma.tum.de/de/personen/tim-hoffmann.html

#### Dr. Andrew O'Shea Sageman-Furnas   +

Projects: C01
University: TU Berlin, Institut für Mathematik, MA 879
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31429486
E-Mail: aosafu[at]math.tu-berlin.de
Website: https://page.math.tu-berlin.de/~aosafu/