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SUMMARY:The injectivity radius of hyperbolic surfaces and some Morse funct
 ions over moduli spaces.
DTSTART:20151125T163000
DTEND:20151125T173000
DTSTAMP:20261001T181725Z
UID:fc00fd8dae40fa3a640d8c7fc950b20a852a195236c407c2899c7a31
CATEGORIES:Conferences - Seminars
DESCRIPTION:Matthieu Gendulphe (Roma)\nLet X be a compact hyperbolic surfa
 ce. 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).\nThe extrema 
 of the injectivity radius have been widely studied using different methods
 .\nSchmutz and Bavard have developed a variational framework for the study
  of min_p R_p(X) as a function over the Teichmüller space.\nBavard and De
 blois have used some geometric decompositions to bound max_p R_p(X) in ter
 ms of the topology of X.\nIn this talk I will present a variational approa
 ch for the study of the injectivity radius\, seen as a function over the T
 eichmüller space of hyperbolic surfaces with a marked point.\nI 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 inequalitie
 s due to Bavard and Deblois.
LOCATION:
STATUS:CONFIRMED
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