107,461 research outputs found
Weak uncertainty principle for fractals, graphs and metric measure spaces
We develop a new approach to formulate and prove the weak uncertainty
inequality which was recently introduced by Okoudjou and Strichartz. We assume
either an appropriate measure growth condition with respect to the effective
resistance metric, or, in the absence of such a metric, we assume the
Poincare inequality and reverse volume doubling property. We also consider
the weak uncertainty inequality in the context of Nash-type inequalities. Our
results can be applied to a wide variety of metric measure spaces, including
graphs, fractals and manifolds
The descriptive theory of represented spaces
This is a survey on the ongoing development of a descriptive theory of
represented spaces, which is intended as an extension of both classical and
effective descriptive set theory to deal with both sets and functions between
represented spaces. Most material is from work-in-progress, and thus there may
be a stronger focus on projects involving the author than an objective survey
would merit.Comment: survey of work-in-progres
Hyperbolic Space Cosmologies
We present a systematic study of accelerating cosmologies obtained from
M/string theory compactifications of hyperbolic spaces with time-varying
volume. A set of vacuum solutions where the internal space is a product of
hyperbolic manifolds is found to give qualitatively the same accelerating
four-dimensional FLRW universe behavior as a single hyperbolic space. We also
examine the possibility that our universe is a hyperbolic space and provide
exact Milne type solutions, as well as intersecting S-brane solutions. When
both the usual 4D spacetime and the m-dimensional internal space are
hyperbolic, we find eternally accelerating cosmologies for , with and
without form field backgrounds. In particular, the effective potential for a
magnetic field background in the large 3 dimensions is positive definite with a
local minimum and thus enhances the eternally accelerating expansion.Comment: 33 pages, 2 figures; v2 refs added; v3 minor change in text, JHEP
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