The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

Riemannian geometry has today become a vast and important subject. This new book of
Marcel Berger sets out to introduce readers to most of the living topics of the field and …

AN UPPER BOUND FOR THE CURVATURE INTEGRAL §1. Introduction Our main result is as
follows. 1.1. Theorem. Let M be a complete Rie Page 1 Algebra i analiz St. Petersburg Math. J …

OPEN MAP THEOREM FOR METRIC SPACES §1. Introduction This paper is a continuation of
[Lytb]. In [Lytb] we discussed the possibil Page 1 Algebra i analiz St. Petersburg Math. J. Tom …

COLLAPSING THREE-DIMENSIONAL CLOSED ALEXANDROV SPACES WITH A LOWER
CURVATURE BOUND Page 1 TRANSACTIONS OF THE AMERICAN MATHEMATICAL …

We classify orthogonal actions of finite groups on Euclidean vector spaces for which the
corresponding quotient space is a topological, homological, or Lipschitz manifold, possibly …

In the present paper, we define a notion of good coverings of Alexandrov spaces with
curvature bounded below, and we prove that every Alexandrov space admits such a good …

Given a compact metric space Z with Hausdorff dimension n, if X is a metric space such that
there exists a distance-nonincreasing onto map f: Z→ X, then the Hausdorff n-volumes …

In a previous paper, we applied Alexandrov geometry methods to study infinite semiplanar
graphs with nonnegative combinatorial curvature. We proved the weak relative volume …

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 …