580 research outputs found
Quasi-symmetric invariant properties of Cantor metric spaces
For metric spaces, the doubling property, the uniform disconnectedness, and
the uniform perfectness are known as quasi-symmetric invariant properties. The
David-Semmes uniformization theorem states that if a compact metric space
satisfies all the three properties, then it is quasi-symmetrically equivalent
to the middle-third Cantor set. We say that a Cantor metric space is standard
if it satisfies all the three properties; otherwise, it is exotic. In this
paper, we conclude that for each of exotic types the class of all the conformal
gauges of Cantor metric spaces has continuum cardinality. As a byproduct of our
study, we state that there exists a Cantor metric space with prescribed
Hausdorff dimension and Assouad dimension.Comment: To appear in Annales de l'Institut Fourie
Boundary correlation numbers in one matrix model
We introduce one matrix model coupled to multi-flavor vectors. The two-flavor
vector model is demonstrated to reproduce the two-point correlation numbers of
boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity
on disk, generalizing the loop operator (resolvent) description. The model can
properly describe non-trivial boundary conditions for the matter Cardy state as
well as for the Liouville field. From this we propose that the n-flavor vector
model will be suited for producing the boundary correlation numbers with n
different boundary conditions on disk.Comment: 16 pages, 3 figures, add elaboration on matter Cardy state and
reference
Large N reduction for Chern-Simons theory on S^3
We study a matrix model which is obtained by dimensional reduction of
Chern-Simon theory on S^3 to zero dimension. We find that expanded around a
particular background consisting of multiple fuzzy spheres, it reproduces the
original theory on S^3 in the planar limit. This is viewed as a new type of the
large N reduction generalized to curved space.Comment: 4 pages, 2 figures, references added, typos correcte
On comeager sets of metrics whose ranges are disconnected
For a metrizable space , we denote by the space of all
metric that generate the same topology of . The space is
equipped with the supremum distance. In this paper, for every strongly
zero-dimensional metrizable space , we prove that the set of all metrics
whose ranges are closed totally disconnected subsets of the line is a dense
subspace in . As its application, we show that
some sets of universal metrics are meager in spaces of metrics.Comment: 13 pages. This paper is published in Topology and its Applications
vol.327 (2023), 10844
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