Surfaces with prescribed curvature in theory and application

• Applicant: Professor Dr. Karsten Grosse-Brauckmann
• Subject Area: Mathematics
• Term: from 2003 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5406715

We are interested in a classical problem of differential geometry, namely surfaces, whose curvatures are constant, or which minimize energies involving curvatures. In a theoretically motivated part, we want to investigate boundaryless surfaces of constant mean curvature in Euclidean and perhaps also in hyperbolic space, in particular under a weakened embeddedness assumption, called Alexandrow-embeddedness. The main question is if the space of these surfaces forms a manifold. Another part is motivated by applications. Triply periodic surfaces arise as interfaces; to determine the exact energies which govern the creation of their morphologies is usually hard. So it seems appropriate to focus on an important example of such an energy, which has hardly been studied: We want to investigate surfaces which minimize the bending energy under a volume constraint. Here, the ultimate goal is a better understanding of as to why the observed morphologies form.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry