29 citations · 92 across the 16 of their papers we have counts for
20 papers
On the geometry of Riemannian isometric embeddings
Dmitri Burago, Hongda Qiu
This note pertains to isometric embeddings endowed with certain geometric properties. We study two embedding problems for a Riemannian manifold which is diffeomorphic to $\RR^n…
Approximations of the connection Laplacian spectra
Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev +1
We consider a convolution-type operator on vector bundles over metric-measure spaces. This operator extends the analogous convolution Laplacian on functions in our earlier work to…
Quantitative stability of Gel'fand's inverse boundary problem
Dmitri Burago, Sergei Ivanov, Matti Lassas +1
In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold with boundary from the knowledge of the bo…
Flexibility of sections of nearly integrable Hamiltonian systems
Dmitri Burago, Dong Chen, Sergei Ivanov
Given any symplectomorphism on which is close to the identity, and any completely integrable Hamiltonian system in the proper dimension, we…
Key ideas behind perturbing any completely integrable Hamiltonian system obtaining volume entropy non-expansiveness
Dmitri Burago, Dong Chen, Sergei Ivanov
This paper is an announcement of a result followed with explanations of some ideas behind. The proofs will appear elsewhere. Our goal is to construct a Hamiltonian perturbation of…
Finsler perturbation with nondense geodesics with irrational directions
Dmitri Burago, Dong Chen
We show that given any Liouville direction and flat Finsler torus, one can make a -small perturbation on an arbitrarily small disc to get a nondense geodesic in the giv…
Examples of exponentially many collisions in a hard ball system
Dmitri Burago, Sergei Ivanov
Consider the system of identical hard balls in moving freely and colliding elastically. We show that there exist initial conditions such that the number of collis…
Feeble fish in time-dependent waters and homogenization of the G-equation
Dmitri Burago, Sergei Ivanov, Alexei Novikov
We study the following control problem. A fish with bounded aquatic locomotion speed swims in fast waters. Can this fish, under reasonable assumptions, get to a desired destination…
A survival guide for feeble fish
Dmitri Burago, Sergei Ivanov, Alexei Novikov
As avid anglers we were always interested in the survival chances of fish in turbulent oceans. This paper addresses this question mathematically. We show that a fish with bounded a…
Spectral stability of metric-measure Laplacians
Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev
We consider a "convolution mm-Laplacian" operator on metric-measure spaces and study its spectral properties. The definition is based on averaging over small metric balls. For reas…
Boundary distance, lens maps and entropy of geodesic flows of Finsler metrics
Dmitri Burago, Sergei Ivanov
We show that a small perturbation of the boundary distance function of a simple Finsler metric on the -disc is also the boundary distance function of some Finsler metric. (Simpl…
A graph discretization of the Laplace-Beltrami operator
Dmitri Burago, Sergei Ivanov, Yaroslav Kurylev
We show that eigenvalues and eigenfunctions of the Laplace-Beltrami operator on a Riemannian manifold are approximated by eigenvalues and eigenvectors of a (suitably weighted) grap…
Polyhedral Finsler spaces with locally unique geodesics
Dmitri Burago, Sergei Ivanov
We study Finsler PL spaces, that is simplicial complexes glued out of simplices cut off from some normed spaces. We are interested in the class of Finsler PL spaces featuring local…
Uniform approximation of metrics by graphs
Dmitri Burago, Sergei Ivanov
We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric s…
Minimality of planes in normed spaces
Dmitri Burago, Sergei Ivanov
We prove that a region in a two-dimensional affine subspace of a normed space has the least 2-dimensional Hausdorff measure among all compact surfaces with the same boundary. F…
On intrinsic geometry of surfaces in normed spaces
Dmitri Burago, Sergei Ivanov
We prove three facts about intrinsic geometry of surfaces in a normed (Minkowski) space. When put together, these facts demonstrate a rather intriguing picture. We show that (1) ge…
Area minimizers and boundary rigidity of almost hyperbolic metrics
Dmitri Burago, Sergei Ivanov
This paper is a continuation of our paper about boundary rigidity and filling minimality of metrics close to flat ones. We show that compact regions close to a hyperbolic one are b…
Topological aspects of the Dvoretzky Theorem
Dmitri Burago, Sergei Ivanov, Serge Tabachnikov
We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
Conjugation-invariant norms on groups of geometric origin
D. Burago, S. Ivanov, L. Polterovich
A group is said to be bounded if it has a finite diameter with respect to any bi-invariant metric. In the present paper we discuss boundedness of various groups of diffeomorphisms.
Separated nets in Euclidean space and Jacobians of biLipschitz maps
Dmitri Burago, Bruce Kleiner
We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous…