Project Details
Projekt
Surfaces of constant mean curvature with non-trivial topology and pluriharmonic maps
Subject Area
Mathematics
Term
from 2003 to 2012
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 5407010
Surfaces of constant mean curvature occur in nature e.g. as membranes in a hole in a wall between two chambers containing gases of different pressure. While the basic theory of such surfaces is well known for a long time, the construction of surfaces with specific "topological" properties has turned out to be very difficult. Based on relatively new mathematical technology we propose to construct exactly such surfaces. We will therefore give particular emphasis to the construction of classes of surfaces occurring in the sciences or in the engineering problems and we will provide geometric visualization of such surfaces. The latter is difficult in itself, since the surfaces are the result of extensive computations involving solutions to differential equations, decompositions of matrices involving some parameters, and automorphic funtions relative to non-trivial fundamental groups.
DFG Programme
Priority Programmes
Subproject of
SPP 1154:
Global Differential Geometry
