Related papers: Convergence and Counting in Infinite Measure

We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two ``splitting in a finite cover'' theorems for isometric group actions on Riemannian manifolds with infinite fundamental groups, where the…

We prove nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in…

For conformal metrics with conical singularities and positive curvature on $\mathbb S^2$, we prove a convergence theorem and apply it to obtain a criterion for nonexistence in an open region of the prescribing data. The core of our study is…

In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are modelled on a finite…

In this work, we describe the asymptotic behavior of complete metrics with prescribed Ricci curvature on open Kahler manifolds that can be compactified by the addition of a smooth and ample divisor. First, we construct a explicit sequence…

We discuss the asymptotic structure of null infinity in five dimensional space-time. Since it is known that the conformal infinity is not useful for odd higher dimensions, we shall employ the coordinate based method like the Bondi…

This paper finds a symmetry relation (between quantiles of a random variable and its negative) that is intuitively appealing. We show this symmetry is quite useful in finding new relations for quantiles, in particular an equivariance…

In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…

We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the…

We show how to define curvature as a measure using the Gauss-Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We find an explicit formula for the curvature measure as a sum…

In this work we construct a sequence of Riemannian metrics on the three-sphere with scalar curvature greater than or equal to $6$ and arbitrarily large widths. Our procedure is based on the connected sum construction of positive scalar…

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our…

In first-passage percolation on the integer lattice, the Shape Theorem provides precise conditions for convergence of the set of sites reachable within a given time from the origin, once rescaled, to a compact and convex limiting shape.…

For any real sequence {c(n)} tending to infinity as n tends to infinity, this constructs a function f which is continuous and integrable, and such that for every nonzero x, limsup c(n) f(n x) is infinite.

We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.

These are classified by the direction of approximation (from above or below), the set family types (partition or covering) of simple functions, the coefficient signature (non-negative or signed), and cardinal number of terms of simple…

In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…

We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential…

We consider the discrepancy of the integer lattice with respect to the collection of all translated copies of a dilated convex body having a finite number of flat, possibly non-smooth, points in its boundary. We estimate the $L^{p}$ norm of…