Related papers: A remark on uniform expansion

Thurston's circle packing approximation of the Riemann Mapping (proven to give the Riemann Mapping in the limit by Rodin-Sullivan) is largely based on the theorem that any topological disk with a circle packing metric can be deformed into a…

We extend the study of \emph{melonic} quartic tensor models to models with arbitrary quartic interactions. This extension requires a new version of the loop vertex expansion using several species of intermediate fields and iterated…

In this paper we study ergodic $\mathbb{Z}^r$-actions and investigate expansion properties along cyclic subgroups. We show that under some spectral conditions there are always directions which expand significantly a given measurable set…

We show that every finite-dimensional Euclidean space contains compact universal differentiability sets of upper Minkowski dimension one. In other words, there are compact sets $S$ of upper Minkowski dimension one such that every Lipschitz…

For $n\geq 25$, we construct a smooth metric $\tilde{g}$ on the standard $n$-dimensional sphere $\mathbb{S}^n$ such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_{k\in\mathbb{N}}$ conformal to $\tilde g$ where each $\tilde…

In this paper, by combining techniques from Ricci flow and algebraic geometry, we prove the following generalization of the classical uniformization theorem of Riemann surfaces. Given a complete noncompact complex two dimensional K\"ahler…

The universal enveloping algebra $\mathscr{U}$ of a two-dimensional nonabelian Lie algebra $L$ is a Lie algebra itself with the commutator as Lie bracket. There exists a presentation of $\mathscr{U}$ with generators $x,y$ and relation…

We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the…

We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riemann-integrable function on a compact interval having limit…

Eternally inflating universes can contain large thermalized regions with different values of the constants of Nature and with different density fluctuation spectra. To find the probability for a `typical' observer to detect a certain set of…

In this paper we extend the dichotomy given by Samuelsson and Wold that can be thought of as an analogue of the Wermer maximality theorem in $\mathbb{C}^2$ for certain polynomial polyhedra. We consider complex non-degenerate simply…

As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…

Opial's inequality and its ramifications play an important role in the theory of differential and difference equations. A sharp unifying generalization of Opial's inequality is presented that contains both its continuous and discrete…

For every affine variety over a global function field, we show that the set of its points with coordinates in an arbitrary rank-one multiplicative subgroup of this function field is topologically dense in the set of its points with…

We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk.…

For a holomorphic function $f$ in the open unit disc $\mathbb{D}$ and $\zeta\in\mathbb{D}$, $S_n(f,\zeta)$ denotes the $n$-th partial sum of the Taylor development of $f$ at $\zeta$. Given an increasing sequence of positive integers…

We consider a version of the open-open game, indicating its connections with universally Kuratowski-Ulam spaces. We show that: Every I-favorable space is universally Kuratowski-Ulam, (Theorem 8); If a compact space Y is I-favorable, then…

The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to…

In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…

Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-\Delta_{1} n+\frac{3}{2} \leq a \leq \Delta_{2} n$ for fixed arbitrary…