Related papers: The Riemannian manifolds with boundary and large s…

We show that a complete Riemannian manifold with boundary is uniquely determined, up to an isometry, by its distance difference representation on the boundary. Unlike previously known results, we do not impose any restrictions on the…

We study the size of the isometry group Isom(M, g) of Riemannian manifolds (M, g) as g varies. For M not admitting a circle action, we show that the order of Isom(M, g) can be universally bounded in terms of the bounds on Ricci curvature,…

In this paper, we develop the infinitesimal geometry of the limit spaces of compact Riemannian manifolds with boundary, where we assume lower bounds on the sectional curvatures of manifolds and boundaries and the second fundamental forms of…

In this paper we generalize a result in [1], showing that an arbitrary Riemannian symmetric space can be realized as a closed submanifold of a covering group of the Lie group defining the symmetric space. Some properties of the subgroups of…

For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also…

A Lie group as a 4-dimensional pseudo-Riemannian manifold is considered. This manifold is equipped with an almost product structure and a Killing metric in two ways. In the first case Riemannian almost product manifold with nonintegrable…

We describe the isometry group of $L^2(\Omega, M)$ for Riemannian manifolds $M$ of dimension at least two with irreducible universal cover. We establish a rigidity result for the isometries of these spaces: any isometry arises from an…

Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for…

Let $M$ be a compact Riemannian manifold with boundary $\pp M$ and $L= \DD+Z$ for a $C^1$-vector field $Z$ on $M$. Several equivalent statements, including the gradient and Poincar\'e/log-Sobolev type inequalities of the Neumann semigroup…

In this paper we give an explicit description of the bounded displacement isometries of a class of spaces that includes the Riemannian nilmanifolds. The class of spaces consists of metric spaces (and thus includes Finsler manifolds) on…

We study isometries in the contact sub-pseudo-Riemannian geometry. In particular we give an upper bound on the dimension of the isometry group of a general sub-pseudo-Riemannian manifold and prove that the maximal dimension is attained for…

The main theorem states that any complete connected Riemannian manifold of bounded geometry can be isometrically realized as a leaf with trivial holonomy in a compact Riemannian foliated space.

We prove that the group of isometries of a metric measure space that satisfies the Riemannian curvature condition, $RCD^*(K,N),$ is in fact a Lie group. We obtain an optimal upper bound on its dimension and classify the spaces where this…

We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups,…

A 4-dimensional Riemannian manifold equipped with an endomorphism of the tangent bundle, whose fourth power is the identity, is considered. The matrix of this structure in some basis is circulant and the structure acts as an isometry with…

We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries…

We establish the equivalence between the family of closed uniformly regular Riemannian manifolds and the class of complete manifolds with bounded geometry.

Developing A.D. Aleksandrov's ideas, the first-named author of this article proposed the following approach to study of rigidity problems for the boundary of a $C^0$-submanifold in a smooth Riemannian manifold: Let $Y_1$ be a 2-dimensional…

We give a classification of many closed Riemannian manifolds M whose universal cover possesses a nontrivial amount of symmetry. More precisely, we consider closed Riemannian manifolds $M$ such that Isom$(\widetilde{M})$ has noncompact…

Given a closed manifold M, we prove the upper bound of (n+d)/2 for the length of a product of systoles that can form a curvature-free lower bound for the total volume of M, in the spirit of M. Gromov's systolic inequalities. Here n is the…