15 jan 2019 -- 16:00
Aula D'Antoni, Roma Tor Vergata
Seminario di Analisi Complessa, Roma Tor Vergata
In this talk we discuss two boundary versions of the Schwarz lemma. The first is for general holomorphic self maps of bounded convex domains with C2 boundary. The second is for biholomorphisms of domains who have an invariant Kahler metric with bounded sectional curvature. The proof of the first relies on some new results about the boundary values of complex geodesics. The proof of the second uses many techniques from Riemannian Geometry: the dynamical behavior of the geodesic flow, deforming metrics using the Ricci flow, injectivity radius estimates, etc.