Project Details
Projekt
FOR 565: Polyhedral Surfaces
Subject Area
Mathematics
Term
from 2005 to 2012
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 5471407
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 withpolytopes, simplicial complexes, etc.) meet and interact.
The goal of the Research Unit is to use and combine the quite unique local expertise in both discrete and differential geometry in order to attack fundamental problems in the area of polyhedral surfaces. Areas to which we will devote considerable joint effort - and in which we expect to make substantial progress - include the following: 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.
The goal of the Research Unit is to use and combine the quite unique local expertise in both discrete and differential geometry in order to attack fundamental problems in the area of polyhedral surfaces. Areas to which we will devote considerable joint effort - and in which we expect to make substantial progress - include the following: 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.
DFG Programme
Research Units
Projects
- Discrete differential geometry of surfaces: special classes and deformations (Applicant Bobenko, Alexander I. )
- Discrete implicit surfaces (Applicant Polthier, Konrad )
- Geometry of discrete integrability (Applicant Bobenko, Alexander I. )
- Non-positive curvature and cubical surfaces (Applicant Joswig, Michael )
- Realization spaces of polyhedral surfaces (Applicant Ziegler, Günter M. )
- Restricting valence for polyhedral surfaces and manifolds (Applicant Sullivan, Ph.D., John M. )
- Spectral curves of polygons and triangulated tori (Applicant Pinkall, Ulrich )
- Zentralprojekt (Applicant Bobenko, Alexander I. )
Spokesperson
Professor Dr. Alexander I. Bobenko
