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SUMMARY:A Bishop-Gromov Type Inequality for some Metric Spaces
DTSTART;VALUE=DATE-TIME:20200106T133000Z
DTEND;VALUE=DATE-TIME:20200106T144500Z
DTSTAMP;VALUE=DATE-TIME:20200224T085423Z
UID:indico-event-5459@indico.math.cnrs.fr
DESCRIPTION:The work concerns a δ-hyperbolic metric space (X\,d) (possibl
y with extra conditions) and the main assumption is that its entropy\, den
oted by H\, is bounded above. Then\, if a subgroup of its isometry group a
cts properly and co-compactly and if D denotes the diameter of the quotien
t\, we will show a Bishop-Gromov type inequality on (X\,d) only in terms o
f δ\, H and D. It is a curvature-free inequality and we will explain how
the bound on the entropy plays the role of a (weak version of a) lower bou
nd on the Ricci curvature and how the δ-hyperbolicity relates to a bound
on the negative part of the sectional curvature. Some consequences of this
inequality are a finiteness theorem as well as a compactness result.\n\nT
his is joint work with G. Courtois\, S. Gallot and A. Sambusetti.\n\nhttps
://indico.math.cnrs.fr/event/5459/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/5459/
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