Speaker
Description
The class of metric surfaces of bounded integral curvature (BIC) is a large class of singular surfaces including e.g. the class of polyhedral surfaces. These surfaces have just enough regularity to define the curvature as a signed Radon measure, and compact BIC surfaces
admit a natural Gauss-Bonnet Theorem. Given a complete surface of bounded integral curvature (without cusps), together with its 2-dimensional Hausdorff measure, I will explain in this talk the basics of local geometric analysis on such spaces: namely, they turn out to be
infinitesimally Hilbertian, intrinsic, locally doubling and locally Poincare. In particular, one obtains a heat kernel on such spaces. We also show that under a global Dynkin-Kato type condition on the negative part of the curvature measure, the above results may be globalized in the natural way.
This is joint work with Sebastian Boldt and Maxime Marot.