Ambartzumian-Pleijel identity in hyperbolic geometry
Date/Time:30 Oct 2019 16:00Venue: S17 #06-11Speaker: Xu Binbin, University of LuxembourgAmbartzumian-Pleijel identity in hyperbolic geometryGiven a convex compact domain in Euclidean plane with C1 boundy, a measure on the space of all straight lines invariant under the isometry group of Euclidean plane induces a distribution on the positive real line, by considering the length of the intersection of straight lines with this domain. Ambartzumian-Pleijel identity is about computing the integral of any real valued C1 function on the positive real line with respect to this distribution. In this talk, we’ll introduce the counterpart of this identity in hyperbolic geometry. Then we will discuss some of its applications. In particular, it can be used to prove Croftin formula and the isoperimetric inequality in hyperbolic geometry. I’ll also discuss some of its generalizations in other context.Add to calendar:
