2 citations · 2 across the 1 of their papers we have counts for
5 papers
Coarse embeddings into a Hilbert space, Haagerup Property and Poincare inequalities
Romain Tessera
We prove that a metric space does not coarsely embed into a Hilbert space if and only if it satisfies a sequence of Poincaré inequalities, which can be formulated in terms of (gene…
Metric sparsification and operator norm localization
Xiaoman Chen, Romain Tessera, Xianjin Wang +1
We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localizat…
Large scale Sobolev inequalities on metric measure spaces and applications
Romain Tessera
We introduce a notion of "gradient at a given scale" of functions defined on a metric measure space. We then use it to define Sobolev inequalities at large scale and we prove their…
Quantitative property A, Poincare inequalities, L^p-compression and L^p-distortion for metric measure spaces
Romain Tessera
We introduce a quantitative version of Property A in order to estimate the L^p-compressions of a metric measure space X. We obtain various estimates for spaces with sub-exponential…
Asymptotic isoperimetry of balls in metric measure spaces
R. Tessera
In this paper, we study the asymptotic behavior of the volume of spheres in metric measure spaces. We first introduce a general setting adapted to the study of asymptotic isoperime…