Related papers: Lower Bounds for non-Archimedean Lyapunov Exponent…

We introduce and study the notion of an outer bi-Lipschitz extension of a map between Euclidean spaces. The notion is a natural analogue of the notion of a Lipschitz extension of a Lipschitz map. We show that for every map $f$ there exists…

Let $F$ be a field of characteristic not $2$ with finitely many square classes. Using combinatorial arguments applied to objects related to vector spaces over finite fields, we deduce an upper bound for the number of Pfister forms over $F$.…

Minimal surfaces in the sub-Riemannian Heisenberg group can be constructed by means of a Riemannian approximation scheme, as limit of Riemannian minimal surfaces. We study the regularity of Lipschitz, non-characteristic minimal surfaces…

Let $\{u_\lambda\}$ be a sequence of $L^2$-normalized Laplacian eigenfunctions on a compact two-dimensional smooth Riemanniann manifold $(M,g)$. We seek to get an $L^p$ restriction bounds of the Neumann data $ \lambda^{-1} \partial_\nu…

We obtain sharp bounds for the modulus of continuity of the uncentered maximal function in terms of the modulus of continuity of the given function, via integral formulas. Some of the results deduced from these formulas are the following:…

This paper is devoted to the study of $L_{p}$ Lyapunov-type inequalities ($ \ 1 \leq p \leq +\infty$) for linear partial differential equations at radial higher eigenvalues. More precisely, we treat the case of Neumann boundary conditions…

We discuss asymptotics for the boundary of critical Boltzmann planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with parameter $\alpha \in (1,2)$.…

Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…

Let $\phi$ be a conformal map of the unit disk onto a domain $D$, and suppose $\phi$ has a boundary extension. We show that arbitrarily good approximations of the boundary extension of $\phi$ can be computed from sufficiently good…

Recent work has shown that statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable, albeit less accurate, estimates of the largest Lyapunov exponent ${\chi}$ in lower-dimensional…

Let M be a von Neumann algebra (not necessarily semi-finite). We provide a generalization of the classical Kadec-Pelczynski subsequence decomposition of bounded sequences in L^p[0,1] to the case of the Haagerup L^p-spaces (1\le p<\infty).…

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph.…

Let $K/F$ be a finite extension of number fields of degree $n \geq 2$. We establish effective field-uniform unconditional upper bounds for the least norm of a prime ideal of $F$ which is degree 1 over $\mathbb{Q}$ and does not ramify or…

We prove an a-priori bound for the Lipschitz constant of a smooth one-phase free boundary graph F(u) in two dimensions. The function u satisfies a fully nonlinear elliptic equation in its positive side, and the gradient of u is equal to 1…

Let $G$ be a finite group and $P$ a Sylow $2$-subgroup of $G$. We obtain both asymptotic and explicit bounds for the number of odd-degree irreducible complex representations of $G$ in terms of the size of the abelianization of $P$. To do…

We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…

Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…

If E is a flat bundle of rank r over a K\"ahler manifold X, we define the Lyapunov spectrum of E: a set of r numbers controlling the growth of flat sections of E, along Brownian trajectories. We show how to compute these numbers, by using…

Let K be a non-archimedean field, and let f in K(z) be a polynomial or rational function of degree at least 2. We present a necessary and sufficient condition, involving only the fixed points of f and their preimages, that determines…

In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in…