buondì,
vi annuncio un semiario di geometria per giovedì prossimo.
a presto,
Bruno
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SEMINARI DI GEOMETRIA
Thursday, December 3, 2015, ore 16:00
Aula: Sala Seminari (Dip. Matematica)
Matthieu Gendulphe (Università di Roma "La Sapienza")
The injectivity radius of hyperbolic surfaces and some Morse functions
over moduli spaces
Let X be a compact hyperbolic surface. The injectivity radius at a
point p of X is the radius of the largest embedded metric ball
centered at p, we denote it by R_p(X).
The extrema of the injectivity radius have been widely studied using
different methods.
Schmutz and Bavard have developed a variational framework for the
study of min_p R_p(X) as a function over the Teichmüller space.
Bavard and Deblois have used some geometric decompositions to bound
max_p R_p(X) in terms of the topology of X.
In this talk I will present a variational approach for the study of
the injectivity radius, seen as a function over the Teichmüller space
of hyperbolic surfaces with a marked point.
I will show that this function is almost a Morse function, and I will
determine all its critical points. As a consequence I will obtain some
known inequalities due to Bavard and Deblois.