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.