Related papers: Convergence and Counting in Infinite Measure
For metric spaces with curvature less than or equal to x, x<0, it is shown that a recurrent geodesic can be approximated by closed geodesics. A counter example is provided for the converse.
We introduce a class of countable groups by some abstract group-theoretic conditions. It includes linear groups with finite amenable radical and finitely generated residually finite groups with some non-vanishing $\ell^2$-Betti numbers that…
The total curvature of complex hypersurfaces in $\bC^{n+1}$ and its variation in families appear to depend not only on singularities but also on the behaviour in the neighbourhood of infinity. We find the asymptotic loss of total curvature…
Complete constant positive scalar curvature metrics on S^n - {p_1, ..., p_k} admit a definite asymptotic structure; i.e. the metric is asymptotic to a specific S^{n-1}-invariant metric near the puncture points. This allows one to glue…
We use certain Morse functions to construct conformal metrics with negative sectional curvature on locally conformally flat manifolds with boundary. Moreover, without conformally flatness assumption, we also construct conformal metric of…
We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers,…
We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…
We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a…
We give a general procedure for gluing together possibly noncompact manifolds of constant scalar curvature which satisfy an extra nondegeneracy hypothesis. Our aim is to provide a simple paradigm for making `analytic' connected sums. In…
We investigate isoperimetric constants of infinite tessellating metric graphs. We introduce a curvature-like quantity, which plays the role of a metric graph analogue of discrete curvature notions for combinatorial tessellating graphs. We…
We introduce the notion of negative topological dimension and the notion of weight for the asymptotic topological dimension. Quantizing of spaces of negative dimension is applied to linguistic statistics.
The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence for nets in Riesz spaces by using the finite additive measures on…
On the space of unimodular lattices, we construct a sequence of invariant probability measures under a singular diagonal element with high entropy and show that the limit measure is 0.
Counting integer points in large convex bodies with smooth boundaries containing isolated flat points is oftentimes an intermediate case between balls (or convex bodies with smooth boundaries having everywhere positive curvature) and cubes…
Motivated by a recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with the real line admits a complete metric of bounded negative sectional curvature…
A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study whether these metrics have negative Ricci curvatures. Affirmatively, we prove…
The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
In this paper, we characterize the congruences of an arbitrary i--lattice, investigate the structure of the lattice they form and how it relates to the structure of the lattice of lattice congruences, then, for an arbitrary non--zero…
The problem of constructing lattices such that their quantization noise approaches a desired distribution is studied. It is shown that asymptotically is the dimension, lattice quantization noise can approach a broad family of distribution…