272 citations · 1.4k across the 38 of their papers we have counts for
38 papers
Regular Ultrametric Skeletons
Manor Mendel
The ultrametric skeleton theorem extracts from every compact metric probability space a subset of ultrametric distortion that carries a measure whose balls are c…
An optimal algorithm for average distance in typical regular graphs
Alexandros Eskenazis, Manor Mendel, Assaf Naor
We design a deterministic algorithm that, given points in a \emph{typical} constant degree regular~graph, queries distances to output a constant factor approximation to…
Dvoretzky-type theorem for Ahlfors regular spaces
Manor Mendel
It is proved that for any , any bounded Ahlfors -regular space contains a -regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most $…
A simple proof of Dvoretzky-type theorem for Hausdorff dimension in doubling spaces
Manor Mendel
The ultrametric skeleton theorem [Mendel, Naor 2013] implies, among other things, the following nonlinear Dvoretzky-type theorem for Hausdorff dimension: For any , any compa…
Nonpositive curvature is not coarsely universal
Alexandros Eskenazis, Manor Mendel, Assaf Naor
We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question of Gromov (1993) and is in contrast to the fact that…
A Simple proof of Johnson-Lindenstrauss extension theorem
Manor Mendel
Johnson and Lindenstrauss proved that any Lipschitz mapping from an -point subset of a metric space into Hilbert space can be extended to the whole space, while increasing the L…