Curvature measure for fractals and application in pattern recognition

• Applicant: Professorin Dr. Martina Zähle
• Subject Area: Mathematics
• Term: from 2008 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 61396530

In the previous period of our project we were able to determine fractal curvatures for rather general self-similar and self-conformal sets. The recent combination with ergodic theory of dynamical systems, which leads to simpler methods of proof, is planned to be further developed. A main aim consists now in extension to new classes, in particular, V-variable and graph directed random fractals.Furthermore, relationships to analysis on fractals and their curvature properties will be investigated, like known from the classical case of spectral behavior and heat kernels. Here connections to potential theory arise via Dirichlet forms. We also intend to support the further development of a computer program for approximations of fractal curvatures with applications.

• DFG Programme: Research Grants