47,800 research outputs found
Distortion of imbeddings of groups of intermediate growth into metric spaces
For every metric space in which there exists a sequence of
finite groups of bounded-size generating set that does not embed coarsely, and
for every unbounded, increasing function , we produce a group of
subexponential word growth all of whose imbeddings in have
distortion worse than .
This applies in particular to any B-convex Banach space , such as
Hilbert space.Comment: Used to appear as first half of arXiv:1403.558
Poisson-Furstenberg boundary and growth of groups
We study the Poisson-Furstenberg boundary of random walks on permutational
wreath products. We give a sufficient condition for a group to admit a
symmetric measure of finite first moment with non-trivial boundary, and show
that this criterion is useful to establish exponential word growth of groups.
We construct groups of exponential growth such that all finitely supported (not
necessarily symmetric, possibly degenerate) random walks on these groups have
trivial boundary. This gives a negative answer to a question of Kaimanovich and
Vershik.Comment: 24 page
Foreword: Of Lawyers, Leaders, and Returning Riddles in Sovereign Debt
This volume contains the research and recollections of more than a doze
Positive solutions for singularly perturbed nonlinear elliptic problem on manifolds via Morse theory
Given (M, g0) we consider the problem -{\epsilon}^2Delta_{g0+h}u + u =
(u+)^{p-1} with ({\epsilon}, h) \in (0, {\epsilon}0) \times B{\rho}. Here
B{\rho} is a ball centered at 0 with radius {\rho} in the Banach space of all
Ck symmetric covariant 2-tensors on M. Using the Poincar\'e polynomial of M, we
give an estimate on the number of nonconstant solutions with low energy for
({\epsilon}, h) belonging to a residual subset of (0, {\epsilon}0) \times
B{\rho}, for ({\epsilon}0, {\rho}) small enough
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