Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Two boundary rigidity results for holomorphic maps

Andrew Zimmer

created by daniele on 09 Jan 2019

15 jan 2019 -- 16:00

Aula D'Antoni, Roma Tor Vergata

Seminario di Analisi Complessa, Roma Tor Vergata

Abstract.

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.

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