DFG-GACR Project: Curvature Measures and Integral Geometry
German-Czech cooperation in the framework of an agreement between the German Science Foundation and the Czech Science Foundation.
Jan Rataj (Charles University, Prag)
Dusan Pokorny (Prag)
The project aims to advance the investigation of curvature measures in d-dimensional Euclidean space in two main directions. So far curvature measures have been introduced only for sets satisfying some basic regularity properties, at least if additivity and other basic properties are required. For more general sets, it is desirable to study curvature measures of approximations to these sets, for instance by parallel sets, as well as the asymptotic behaviour of these approximations. This idea has proved to be fruitful already for certain fractal sets and it will be further explored in the project. Furthermore, the classical curvature measures are defined as measures on the (generalized) normal bundle of closed convex (or more general) sets. In view of integral representations of classical functionals in convex geometry, such as mixed volumes, it seems to be necessary to extend the notion of a curvature measure to boundary manifolds of higher order (flag manifolds). Corresponding flag measures have already been useful in special situations, a general investigation has not been carried out up to now and will be pursuit in the project.
Financing / Duration of the project
Financing: German Science Foundation (DFG) / Czech Science Foundation (GACR)
Duration: 2010 - 2013