Detailseite
Geometric curvature energies
Antragsteller
Professor Dr. Heiko von der Mosel
Fachliche Zuordnung
Mathematik
Förderung
Förderung von 2007 bis 2013
Projektkennung
Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 64980826
The central issue of this research proposal is the study of geometric curvature energies on curves, surfaces, and higher-dimensional objects of low regularity. These energies exhibit self-avoidance and regularizing effects: a finite energy level guarantees and quantifies embeddedness of the geometric object, and leads to higher regularity. There is a variety of geometric curvature energies ranging from hard steric constraints to soft repulsive potentials, such as global curvature, integral versions of Menger curvature, or self-repulsive knot energies. We investigate the analytical properties of these energies and study their behaviour on families of curves or surfaces. The results will be applied to topologically constrained variational problems in the class of embeddings, and we examine the corresponding timedependent geometric flow problems.
DFG-Verfahren
Sachbeihilfen
Internationaler Bezug
Polen
Beteiligte Person
Professor Dr. Pawel Strzelecki