3,005 research outputs found
Vector ultrametric spaces and a fixed point theorem for correspondences
In this paper, vector ultrametric spaces are introduced and a fixed point
theorem is given for correspondences. Our main result generalizes a known
theorem in ordinary ultrametric spaces.Comment: 8 page
Equivariant Elliptic Genera and Local McKay Correspondences
We prove an equivariant version of the McKay correspondence for the elliptic
genus on open varieties with a torus action. As a consequence, we will prove
the equivariant DMVV formula for the Hilbert scheme of points on \C^2
The role of regularity to reach the vector valued version of Caristi's fixed point theorem
In this paper we discuss on the vector valued version of Caristi's theorem.
We show that the regularity of the cone is an essential condition to reach the
vector valued version of Caristi's theorem in vector valued metric spaces. It
is shown that how the absence of the regularity causes some previous Caristi
type theorems and results fail to be correct. Our main result give a vector
valued version of Caristi's theorem for correspondences with weakened
hypotheses in comparison with previous results and generalize them.Comment: This paper will be published in the "Journal of Nonlinear and Convex
Analysis (JNCA)" 0n 2015. Due to the JNCA's publication policy, the paper has
been withdrawn by the author
Isometry Group of Gromov--Hausdorff Space
The present paper is devoted to investigation of the isometry group of the
Gromov-Hausdorff space, i.e., the metric space of compact metric spaces
considered up to an isometry and endowed with the Gromov-Hausdorff metric. The
main goal is to present a proof of the following theorem by George Lowther
(2015): The isometry group of the Gromov-Hausdorff space is trivial.
Unfortunately, the author himself has not publish an accurate text for 2 years
passed from the publication of draft (that is full of excellent ideas mixed
with unproved and wrong statements) in the https://mathoverflow.net/ blog (see
the exact reference in he bibliography).Comment: 28 pages, 4 figures, 13 bib item
Exact triangle for fibered Dehn twists
We use quilted Floer theory to generalize Seidel's long exact sequence in
symplectic Floer theory to fibered Dehn twists. We then apply it to construct
versions of the Floer and Khovanov-Rozansky exact triangles in Lagrangian Floer
theory of moduli spaces of bundles.Comment: This version (postpublication) addresses a sign issue on p. 4
Singular Geometry and Higgs Bundles in String Theory
This brief survey aims to set the stage and summarize some of the ideas under
discussion at the Workshop on Singular Geometry and Higgs Bundles in String
Theory, to be held at the American Institute of Mathematics from October 30th
to November 3rd, 2017. One of the most interesting aspects of the duality
revolution in string theory is the understanding that gauge fields and matter
representations can be described by intersection of branes. Since gauge theory
is at the heart of our description of physical interactions, it has opened the
door to the geometric engineering of many physical systems, and in particular
those involving Higgs bundles. This note presents a curated overview of some
current advances and open problems in the area, with no intention of being a
complete review of the whole subject
A-infinity functors for Lagrangian correspondences
We construct A-infinity functors between Fukaya categories associated to
monotone Lagrangian correspondences between compact symplectic manifolds. We
then show that the composition of A-infinity functors for correspondences is
homotopic to the functor for the composition, in the case that the composition
is smooth and embedded.Comment: 84 pages, 20 figures. To appear in Selecta Mat
Gluing pseudoholomorphic quilted disks
We construct families of quilted surfaces parametrized by the multiplihedra,
and define moduli spaces of pseudoholomorphic quilted disks using the theory of
pseudoholomorphic quilts of Wehrheim and Woodward. We prove a gluing theorem
for regular, isolated pseudoholomorphic quilted disks. This analytical result
is a fundamental ingredient for the construction of A-infinity functors
associated to Lagrangian correspondences.Comment: 69 pages, 14 figure
Generalized Vector Quasi-Equilibrium Problems Involving Relaxed Continuity of the Set-Valued Maps
In this paper, we study the existence of solutions for generalized vector
quasi-equilibrium problems. Firstly, we prove that in the case of Banach
spaces, the assumptions of continuity over correspondences can be weakened. The
theoretical analysis is based on fixed-point theorems. Secondly, we establish
new equilibrium theorems as applications of the KKM principle.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1605.0301
A new survey: Cone metric spaces
The purpose of this new survey paper is, among other things, to collect in
one place most of the articles on cone (abstract, K-metric) spaces, published
after 2007. This list can be useful to young researchers trying to work in this
part of functional and nonlinear analysis. On the other hand, the existing
review papers on cone metric spaces are updated.
The main contribution is the observation that it is usually redundant to
treat the case when the underlying cone is solid and non-normal. Namely, using
simple properties of cones and Minkowski functionals, it is shown that the
problems can be usually reduced to the case when the cone is normal, even with
the respective norm being monotone. Thus, we offer a synthesis of the
respective fixed point problems arriving at the conclusion that they can be
reduced to their standard metric counterparts. However, this does not mean that
the whole theory of cone metric spaces is redundant, since some of the problems
remain which cannot be treated in this way, which is also shown in the present
article.Comment: 27 page
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