“Geometric calculus of variations and partial differential equations” at the University of Vienna
This is the webpage of the research group «Geometric Calculus of Variations and Partial Differential Equations» at the University of Vienna.
We study optimal shapes for geometric problems such as least length, least area, or least bending energy as well as the rich interplay of these shapes with the global geometry and topology of their ambient spaces or the physics modelled by these spaces.
These optimal shapes may be described by partial differential equations, which have lives of their own. The study of these equations interweaving analytical and geometric techniques is an important part of the research carried out in our group.
We also study the global shape of spaces whose geometry is locally constrained by upper or lower bounds on the curvature or by qualitative geometric descriptions of such curvature bounds.
Relaxing the former condition by the latter allows for powerful compactness results, where limit spaces may not be smooth but retain enough structure to gain deep geometric insights.