DFG Research Unit


Project HeadsAlexander I. Bobenko (Coordinator)Michael Joswig Ulrich Pinkall Konrad Polthier John M. Sullivan Günter M. Ziegler (Deputy coordinator) OverviewThe 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 quadmeshes and quadsurfaces), 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: Nonpositive 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. Moreover there are several related applicationprojects within the DFGResearch Center Matheon, in particular Projects F1, F4 and F5.
