相关论文: Alexandrov spaces with maximal number of extremal …

The equivariant Gromov--Hausdorff convergence of metric spaces is studied. Where all isometry groups under consideration are compact Lie, it is shown that an upper bound on the dimension of the group guarantees that the convergence is by…

We extend the equivariant classification results of Escher and Searle for closed, simply connected, non-negatively curved Riemannian $n$-manifolds admitting isometric isotropy-maximal torus actions to the class of such manifolds admitting…

We prove several rigidity properties for random quotients of mapping class groups of surfaces, namely whose kernel is normally generated by the n-th steps of finitely many independent random walks. Firstly, we generalise a celebrated…

The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The characterization of its extremal bodies is a long-standing open…

We specify a result of Yokoi \cite{yo} by proving that if $G$ is an abelian group and $X$ is a homogeneous metric $ANR$ compactum with $\dim_GX=n$ and $\check{H}^n(X;G)\neq 0$, then $X$ is an $(n,G)$-bubble. This implies that any such space…

We find conditions under which the pretangent spaces to general metric spaces have the nonpositive Aleksandrov curvature or nonnegative one. The infinitesimal structure of general metric cpaces with Busemann convex pretangent spaces is also…

Let $X$ be a minuscule homogeneous space, an odd quadric, or an adjoint homogenous space of type different from $A$ and $G_2$. Le $C$ be an elliptic curve. In this paper, we prove that for $d$ large enough, the scheme of degree $d$…

Equipped with the L^2-distortion distance, the space "X" of all metric measure spaces (X,d,m) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of…

We give a characterization of those Alexandrov spaces admitting a cohomogeneity one action of a compact connected Lie group $G$ for which the action is Cohen--Macaulay. This generalizes a similar result for manifolds to the singular setting…

This article resolves several long-standing conjectures about Artin groups of euclidean type. In particular, we prove that every irreducible euclidean Artin group is a torsion-free centerless group with a decidable word problem and a…

During the years 1940-1970, Alexandrov and the "Leningrad School" have investigated the geometry of singular surfaces in depth. The theory developed by this school is about topological surfaces with an intrinsic metric for which we can…

In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an extremal function of the critical Hardy inequality under…

In each dimension of the form $4n-1$ with $n\geq 3$, we construct infinitely many new examples of manifolds admitting metrics with positive sectional curvature almost everywhere. In addition, we show that if $n\geq 6$, infinitely many of…

We show that if an Alexandrov space $X$ has an Alexandrov subspace $\bar \Omega$ of the same dimension disjoint from the boundary of $X$, then the topological boundary of $\bar \Omega$ coincides with its Alexandrov boundary. Similarly, if a…

It is well known that the only surfaces that are simultaneously minimal in $\mathbb{R}^3$ and maximal in $\mathbb{L}^3$ are open pieces of helicoids (in the region in which they are spacelike) and of spacelike planes (O. Kobayashi 1983).…

It was proved by Brudno that entropy and Kolmogorov complexity for dynamical systems are tightly related. We generalize his results to the case of arbitrary computable amenable group actions. Namely, for an ergodic shift-action, the…

We consider an infinitesimal version of the Bishop-Gromov relative volume comparison condition as generalized notion of Ricci curvature bounded below for Alexandrov spaces. We prove a Laplacian comparison theorem for Alexandrov spaces under…

We study balls of homogeneous cubics on $\mathbb R^n$, $n = 2,3$, which are bounded by unity on the unit sphere. For $n = 2$ we completely describe the facial structure of this norm ball, while for $n = 3$ we classify all extremal points…

In this article, we study rectifying curves in arbitrary dimensional Euclidean space. A curve is said to be a rectifying curve if, in all points of the curve, the orthogonal complement of its normal vector contains a fixed point. We…

In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of…