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It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact K¨ahler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of ...
The purpose of this note is to present an extension and an alternative proof to Theorem 1.3 from G. Battle (Appl. Comput. Harmonic Anal. 4 (1997) 119–146). This extension applies to wavelet Bessel set...
This paper consists of three parts, each devoted to a result due to J.-C. Yoccoz.The proofs are all somewhat modied, but they are also deeply in!uenced byYoccoz's work.
Let T be a locally finite simplicial tree and let ! ⊂ Aut(T ) be a finitely generated discrete subgroup. We obtain an explicit formula for the critical exponent of the Poincare series associated...
An important well-known result of Rota describes the relationship between the M¨obius functions of two posets related by a Galois connection. We present an analogous result relating the antipodes of...
Abstract: Let (G, *) be a semigroup, D subset of G, and n >= 2 be an integer. We say that (D, *) is an n-closed subset of G if a_1* ... *a_n in D for every a_1, ..., a_n in D. Hence every closed set i...
Dendroidal sets offer a formalism for the study of 1-operads akin to the formalism of 1-categories by means of simplicial sets. We present here an account of the current state of the theory while plac...
We show that any open set in Rn is a union of an ascending sequence of bounded open sets with analytic boundary.This is just a technical result, which is probably known. We be-lieve, however, that it ...
The aim of this paper is to estimate the L2-norms of vector-valued Riesz trans-forms Rs  and the norms of Riesz operators on Cantor sets in Rd, as well as to study the distribution of values of Rs ...
For any irrational number , there exists an ergodic area preserv-ing homeomorphism of the closed annulus which is isotopic to the identitity,admits no compact invariant set contained in the interior ...
It is well known that for a > 4, the dynamical behaviors of the logistic map fa(x) = ax(1 − x) on the maximal invariant compact set are “simple”, which could be clearly explained by the theories...
It is well-known that the Julia set J(f) of a rational map f : C → C is uniformly perfect; that is, every ring domain which separates J(f) has bounded modulus,with the bound depending only on f. In th...
We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if $A\subset\mathbb{R}^d$ is convex and the origin $0\in A$, then for any ball $B$ centered at the origin...
We propose the notion of integral Menger curvature for $m$-dimensional sets in $n$-dimensional Euclidean space and prove that finiteness of this quantity implies Ahlfors regularity with constant depe...

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