[Dottorcomp] avviso di seminario, 17 marzo ore 17 (Oliver Roth, University of Wuerzburg)

[Lorenzo Tamellini]

Buongiorno a tutt*

scusandomi con chi avesse gia` ricevuto questo avviso da altre mailing
list, inoltro l'avviso di seminario qui sotto, dalla sezione di Geometria
del dipartimento di Matematica del Politecnico di Milano.

Cordiali saluti,
Lorenzo Tamellini

=====================================

Si avvisa che in data 17/3/2021, alle ore 17:00, On line, nell'ambito delle
iniziative della sezione di Geometria, si svolgerà il seguente seminario:

A new Schwarz-Pick Lemma at the boundary and rigidity of holomorphic maps
Oliver Roth, University of Wuerzburg
We establish several invariant boundary versions of the (infinitesimal)
Schwarz-Pick lemma for conformal pseudometrics on the unit disk and for
holomorphic selfmaps of strongly convex domains in CN in the spirit of the
boundary Schwarz lemma of Burns-Krantz.

Firstly, we focus on the case of the unit disk and prove a general boundary
rigidity theorem for conformal pseudometrics with variable curvature. In
its simplest cases this result already includes new types of boundary
versions of the lemmas of Schwarz-Pick, Ahlfors-Schwarz and Nehari-Schwarz.
The proof is based on a new Harnack-type inequality as well as a boundary
Hopf lemma for conformal pseudometrics which extend earlier interior
rigidity results of Golusin, Heins, Beardon, Minda and others. Secondly, we
prove similar rigidity theorems for sequences of conformal pseudometrics,
which even in the interior case appear to be new. For instance, a first
sequential version of the strong form of Ahlfors\' lemma is obtained.

As an auxiliary tool we establish a Hurwitz-type result about preservation
of zeros of sequences of conformal pseudometrics.

Thirdly, we apply the one-dimensional sequential boundary rigidity results
together with a variety of techniques from several complex variables to
prove a boundary version of the Schwarz-Pick lemma for holomorphic maps of
strongly convex domains in $\\C^N$ for $N>1$.



È gradita la sua partecipazione.
Cordiali saluti.
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