257 research outputs found
Extremal Vanishing Horizon Kerr-AdS Black Holes at Ultraspinning Limit
By utilizing the ultraspinning limit we generate a new class of extremal
vanishing horizon (EVH) black holes in odd dimensions (). Starting from
the general multi-spinning Kerr-AdS metrics, we show the EVH limit commutes
with the ultraspinning limit, in which the resulting solutions possess a
non-compact but finite area manifold for all slices. We
also demonstrate the near horizon geometries of obtained ultraspinning EVH
solutions contain an AdS throats, where it would be a BTZ black hole in the
near EVH cases. The commutativity of the ultraspinning and near horizon limits
for EVH solutions is confirmed as well. Furthermore, we discuss only the
five-dimensional case near the EVH point can be viewed as a super-entropic
black hole. We also show that the thermodynamics of the obtained solutions
agree with the BTZ black hole. Moreover we investigate the EVH/CFT proposal,
demonstrating the entropy of d dual CFT and Bekenstein-Hawking entropy are
equivalent.Comment: 29 pages, 3 figures, references added, typos corrected, revised
version to match published versio
An isoperimetric inequality for uniformly log-concave measures and uniformly convex bodies
We prove an isoperimetric inequality for the uniform measure on a uniformly
convex body and for a class of uniformly log-concave measures (that we
introduce). These inequalities imply (up to universal constants) the
log-Sobolev inequalities proved by Bobkov--Ledoux as well as the isoperimetric
inequalities due to Bakry-Ledoux and Bobkov--Zegarlinski. We also recover a
concentration inequality for uniformly convex bodies, similar to that proved by
Gromov--Milman.Comment: 39 page
Isoperimetric and Concentration Inequalities - Equivalence under Curvature Lower Bound
It is well known that isoperimetric inequalities imply in a very general
measure-metric-space setting appropriate concentration inequalities. The former
bound the boundary measure of sets as a function of their measure, whereas the
latter bound the measure of sets separated from sets having half the total
measure, as a function of their mutual distance. We show that under a lower
bound condition on the Bakry--\'Emery curvature tensor of a Riemannian manifold
equipped with a density, completely general concentration inequalities imply
back their isoperimetric counterparts, up to dimension \emph{independent}
bounds. As a corollary, we can recover and extend all previously known
(dimension dependent) results by generalizing an isoperimetric inequality of
Bobkov, and provide a new proof that under natural convexity assumptions,
arbitrarily weak concentration implies a dimension independent linear
isoperimetric inequality. Further applications will be described in a
subsequent work. Contrary to previous attempts in this direction, our method is
entirely geometric, continuing the approach set forth by Gromov and adapted to
the manifold-with-density setting by Morgan.Comment: 28 pages; to appear in Duke Math. J. - shortened exposition and
addressed referees' useful comment
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