Diff. Geom, Math. Phys., PDE Seminar: Philippe Castillon

Harmonic manifolds are those Riemannian manifolds whose harmonic functions satisfy the mean-value property, or equivalently, whose spheres have constant mean curvature. F. Ledrappier introduced an asymptotic version of harmonicity which was mainly studied in the cocompact and homogeneous cases. In this talk, I will review some classical facts on harmonic manifolds and prove some new results on asymptotically harmonic manifolds, including a characterization in term of the volume form . This is a joint work with Andrea Sambusetti.