Related papers: Non-Hilbertian tangents to Hilbertian spaces

In this paper, we consider different types of non-positive curvature properties of the Hilbert metric of a convex domain in R^n. First, we survey the relationships among the concepts and prove that in the case of Hilbert metric some of them…

We investigate certain geometric properties of the spaces of idempotent measures. In particular, we prove that the space of idempotent measures on an infinite compact metric space is homeomorphic to the Hilbert cube.

A finitely-additive measure $\lambda $ on an infinite-dimensional real Hilbert space $E$ which is invariant with respect to shifts and orthogonal mappings has been defined. This measure can be considered as the analog of the Lebesgue…

We construct the first example of a coarsely non-amenable (= without Guoliang Yu's property A) metric space with bounded geometry which coarsely embeds into a Hilbert space.

We show that in any infinitesimally Hilbertian $CD^*(K,N)$-space at almost every point there exists a Euclidean weak tangent, i.e. there exists a sequence of dilations of the space that converges to a Euclidean space in the pointed measured…

Kuelbs-Steadman spaces are introduced in this article on a separable metric space with finite diameter and finite positive Borel measure. Kuelbs-Steadman spaces of the Lipschitz type are also discussed. Various inclusion properties are also…

We construct a non-doubling measure on the real line, all tangent measures of which are equivalent to Lebesgue measure.

We investigate the asymptotic geometry of Hermitian non-K\"ahler Ricci-flat metrics with finite $\int|Rm|^2$ at infinity. Specifically, we prove: 1. Any such metric is asymptotic to an ALE, ALF-A, AF, skewed special Kasner, ALH* model at…

We prove infinitesimal rigidity and integrability of the moduli space for Hermitian gravitational instantons. Together with the recent proof by Biquard, Gauduchon, and LeBrun of local rigidity for Hermitian instantons, this completes the…

We show that, given a metric space $(Y,d)$ of curvature bounded from above in the sense of Alexandrov, and a positive Radon measure $\mu$ on $Y$ giving finite mass to bounded sets, the resulting metric measure space $(Y,d,\mu)$ is…

In this paper, we propose the study of a conjecture whose affirmative solution would provide an example of a non-convex Chebyshev set in an infinite-dimensional real Hilbert space.

The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infinite locally finite graphs excluding a minor…

We study symplectic groups and indefinite orthogonal groups over involutive, possibly noncommutative, algebras $(A, \sigma)$. In the case when the algebra $(A, \sigma)$ is Hermitian, or the complexification $(A_{\mathbb{C}},…

We find a new class of invariant metrics existing on the tangent bundle of any given almost-Hermitian manifold. We focus here on the case of Riemannian surfaces, which yield new examples of K\"ahlerian Ricci-flat manifolds in four real…

We consider the homogeneous space $M=H\times H/\Delta K$, where $H/K$ is an irreducible symmetric space and $\Delta K$ denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of $H\times H$-invariant…

This is a brief survey of some recent developments in the study of infinite dimensional Hopf algebras which are either noetherian or have finite Gelfand-Kirillov dimension. A number of open questions are listed.

We give new examples of weak Hilbert spaces.

In any infinite dimensional Hilbert space $\mathcal H$ there exist orthogonal projections $Q_1$, $Q_2$ and $Q_3$, such that a sequence $(P_n... P_1(x))$ diverges in norm for some $P_1,P_2,...\in\{Q_1,Q_2,Q_3\}$ and $x\in\mathcal H$.

In this work we extend many classical results concerning the relationship between densities, tangents and rectifiability to the parabolic spaces, namely $\mathbb{R}^{n+1}$ equipped with parabolic dilations. In particular we prove a…

We provide three new examples of twisted Hilbert spaces by considering properties that are "close" to Hilbert. We denote them $Z(\mathcal J)$, $Z(\mathcal S^2)$ and $Z(\mathcal T_s^2)$. The first space is asymptotically Hilbertian but not…