相关论文: Completeness with respect to the probabilistic Pom…

Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…

Let H be a Hilbert space and let F be the family of all countable subsets of an orthonormal basis of H. We show that if F is infinite then F is equipollent with every linear basis of the vector space H. In doing so we also present a short…

This paper deals with both complex dynamical systems and conformal iterated function systems. We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a $d$-parameter family of…

In this article, we give probabilistic versions of Sobolev embeddings on any Riemannian manifold $(M,g)$. More precisely, we prove that for natural probability measures on $L^2(M)$, almost every function belong to all spaces $L^p(M)$,…

This is the author's Ph.D. thesis, submitted to the University of Leipzig. It deals with the $L^2$ Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold. The main body of the…

We extend some classical results of Bousfield on homology localizations and nilpotent completions to a presentably symmetric monoidal stable $\infty$-category $\mathscr{M}$ admitting a multiplicative left-complete $t$-structure. If $E$ is a…

In this work, we consider sequence of metrics with almost non-negative scalar curvature on torus. We show that if the sequence is uniformly conformal to another sequence of metrics with uniformly controlled geometry, then it converges to a…

We prove a parametric h-principle for complete nonflat conformal minimal immersions of an open Riemann surface $M$ into $\mathbb R^n$, $n\geq 3$. It follows that the inclusion of the space of such immersions into the space of all nonflat…

We find necessary and sufficient conditions for a Lipschitz map $f:\mathbb{R}E\to X$, into a metric space to have the image with the $k$-dimensional Hausdorff measure equal zero, $H^k(f(E))=0$. An interesting feature of our approach is that…

In this paper, we consider a fixed metric space (possibly an oriented Riemannian manifold with boundary) with an increasing sequence of distance functions and a uniform upper bound on diameter. When the metric space endowed with the…

We provide a new quantitative version of Helly's theorem: there exists an absolute constant $\alpha >1$ with the following property: if $\{P_i: i\in I\}$ is a finite family of convex bodies in ${\mathbb R}^n$ with ${\rm int}\left…

The present paper is concerned with Lipschitz properties of convex mappings. One considers the general context of mappings defined on an open convex subset $\Omega$ of a locally convex space $X$ and taking values in a locally convex space…

Given a diagonalizable $N\times N$ matrix $H$, whose non-degenerate spectrum consists of $p$ pairs of complex conjugate eigenvalues and additional $N-2p$ real eigenvalues, we determine all metrics $M$, of all possible signatures, with…

In this paper, we first introduce and study the notion of random Chebyshev centers. Further, based on the recently developed theory of stable sets, we introduce the notion of random complete normal structure so that we can prove the two…

In this paper we focus on the set-open topologies on the group $\mathcal{H}(X)$ of all self-homeomorphisms of a topological space $X$ which yield continuity of both the group operations, product and inverse function. As a consequence, we…

We define a simple criterion for a homogeneous, complete metric structure $X$ that implies that the automorphism group $\mbox{Aut}(X)$ satisfies all the main consequences of the existence of ample generics: it has the small index property,…

We establish a framework to determine the linear completeness of families of non-linear trajectories in Hilbert spaces, which relies on an infinite analytic block Toeplitz operator formulation. By means of this approach, we show the linear…

We characterize measure spaces such that the canonical map $L_\infty \to L_1^*$ is surjective. In case of $d$ dimensional Hausdorff measure of a complete separable metric space $X$ we give two equivalent conditions. One is in terms of the…

Given an extended real-valued submeasure $\nu$ defined on a field of subsets $\Sigma$ of a given set, we provide necessary and sufficient conditions for which the pseudometric $d_\nu$ defined by $d_{\nu}(A,B):=\min\{1,\nu(A\bigtriangleup…

A totally symmetric set is a finite subset of a group for which any permutation of the elements can be realized by conjugation in the ambient group. Such sets are rigid under homomorphisms, and so exert a great deal of control over the…