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SUMMARY:Harmonic Maps for Hitchin Representations
DTSTART;VALUE=DATE-TIME:20190415T143000Z
DTEND;VALUE=DATE-TIME:20190415T154500Z
DTSTAMP;VALUE=DATE-TIME:20190422T105606Z
UID:indico-event-4456@indico.math.cnrs.fr
DESCRIPTION:Hitchin representations are an important class of representati
ons of fundamental groups of closed hyperbolic surfaces into PSL(n\,R)\, a
t the heart of higher Teichmüller theory. Given such a representation j\,
there is a unique j-equivariant harmonic map from the universal cover of
the hyperbolic surface to the symmetric space of PSL(n\,R). We show that i
ts energy density is at least 1 and that rigidity holds. In particular\, w
e show that given a Hitchin representation\, every equivariant minimal imm
ersion from the hyperbolic plane into the symmetric space of PSL(n\,R) is
distance-increasing. Moreover\, equality holds at one point if and only if
it holds everywhere and the given Hitchin representation j is an n-Fuchsi
an representation.\n\nhttps://indico.math.cnrs.fr/event/4456/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/4456/
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