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Quasi-metric antipodal spaces and maximal Gromov hyperbolic spaces
Hyperbolic fillings of metric spaces are a well-known tool for proving results on extending quasi-Moebius maps between boundaries of Gromov...
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Metric Spaces Meet Groups
Studying the close connection between groups and geometry is a central concept in geometric group theory. Groups are equipped with metrics themselves...
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Some Properties of the Topological Entropy of a Family of Dynamical Systems Defined on an Arbitrary Metric Space
AbstractWe consider a family of dynamical systems defined on a noncompact metric space and continuously depending on a parameter varying in some...
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On locally compact groups of small topological entropy
We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the...
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Analysis on Ultra-Metric Spaces via Heat Kernels
AbstractWe give an overview of heat kernels on ultra-metric spaces based on the results of [
9 ] and [11 ]. In particular, we present estimates of the...
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Obstacle Problems on RCD(K, N) Metric Measure Spaces
In this paper, we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds. We show the existence and Lipschitz...
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Complete Metric Spaces
Ascoli–Arzela theorem, completion of a metric space, Banach’s contraction map** theorem and Baire category theorem are the major results discussed....
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Vietoris–Rips metric thickenings of the circle
Vietoris–Rips metric thickenings have previously been proposed as an alternate approach to understanding Vietoris–Rips simplicial complexes and their...
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Banach algebras on locally compact groups
In this chapter, we shall consider the classical Banach algebras of harmonic analysis that are associated with a locally compact group G. The class...
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Sharp uncertainty principles on metric measure spaces
We prove the rigidity of the Heisenberg–Pauli–Weyl uncertainty principle and the Caffarelli–Kohn–Nirenberg interpolation inequality, on metric...
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Nash-Type Inequalities on Metric-Measure Spaces
AbstractWe extend homogeneous and inhomogeneous Nash-type inequalities to abstract metric-measure spaces.
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Locally Compact Spaces
Locally compact spaces and their one-point compactification are studied. Baire’s theorem and a version of Urysohn lemma for locally compact Hausdorff...
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Tameness in generalized metric structures
We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a...
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On the characterization of harmonic functions with initial data in Morrey space
Let ( X, d, μ ) be a metric measure space satisfying the doubling condition and an L 2 -Poincaré inequality. Consider the nonnegative operator
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Point processes, cost, and the growth of rank in locally compact groups
Let G be a locally compact, second countable, unimodular group that is nondiscrete and noncompact. We explore the ergodic theory of invariant point...
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A class of the Newtonian HK-Sobolev spaces on metric measure spaces
In this article, the authors present a systematic study of a class of the Newtonian HK-Sobolev spaces on metric measure spaces. Several Sobolev-type...