DFG Research Unit
Alexander I. Bobenko (Coordinator)
John M. Sullivan
GŁnter M. Ziegler (Deputy coordinator)
The theory of polyhedral surfaces is a very concrete special case (and testing ground) of an active mathematical terrain where differential geometry (providing the classical theory for smooth surfaces) and discrete geometry (concerned with polytopes, simplicial complexes, etc.) meet and interact.
The goal of the research group is to combine discrete and differential geometry in order to attack fundamental problems in the area of polyhedral surfaces. Areas to which we devote considerable joint effort include discrete surfaces of constant mean curvature (including minimal surfaces), discrete notions of curvature, cubical complexes (including quad-meshes and quad-surfaces), and the existence and rigidity of special kinds of polyhedral surfaces. While all of these problems have interest from the pure mathematics standpoint we adopt here, many are also motivated by questions from such diverse settings as computational geometry, mesh generation, and mathematical physics.
There are seven tightly related projects:
Project B1: Discrete differential geometry of surfaces:
special classes and deformations
Project B2: Geometry of discrete integrability
Project JZ: Non-positive curvature and cubical surfaces
Project P: Spectral curves of polygons and triangulated tori
Project Po: Discrete implicit surfaces
Project S: Restricting valence for polyhedral surfaces and manifolds
Project Z: Realization spaces of polyhedral surfaces
If you go to the projects page, you will get an impression of how these different projects are related.