SEMINARIO DI MATEMATICA

mercoledì 28 maggio 2008

ore 16.00

Scuola Normale Superiore

Pisa

(Aula Tonelli)

Alberto Saracco

Università di Milano "Bicocca"

Terrà  un seminario dal titolo:

“Complete hyperbolicity of Lempert's elliptic tubes”

Abstract

Given a domain D of RP^n, Lempert gives a projectively invariant construction for its elliptic tube D^e in CP^n. Moreover D^e is omotopically equivalent to D. In particular it is (simply) connected if and only if D is.For D contained in an affine chart R^n and convex, Lempert gives an explicit formula for the elliptic tube, and a simple example shows that D^e can be non convex. However D^e is a domain of holomorphy if and only if D is convex. In this case D is Hilbert hyperbolic, D^e is Kobayashi hyperbolic, and the Kobayashi distance restriced to D coincides with the Hilbert distance.

In a joint work (in progress) with Daniele Alessandrini, we show that actually if D is convex in an affine chart, D^e is C-convex in the corresponding chart, thus complete hyperbolic and hyperconvex.

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