Geometric and Functional Analysis
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Multiple Recurrence Theorem for Measure Preserving Actions of a Nilpotent Group
Geometric and Functional Analysis - Tập 8 Số 5 - Trang 853-931 - 1998
An isoperimetric inequality for the Heisenberg groups
Geometric and Functional Analysis - Tập 8 - Trang 219-233 - 1998
We show that the Heisenberg groups
$ \cal {H}^{2n+1} $
of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means that each loop of length L bounds a disk of area ~ L
2.) This implies several important results about isoperimetric inequalities for discrete groups that act ......
On the random Chowla conjecture
Geometric and Functional Analysis - Tập 33 - Trang 749-777 - 2023
We show that for a Steinhaus random multiplicative function
$$f:{\mathbb {N}}\rightarrow {\mathbb {D}}$$
and any polynomial
$$P(x)\in {\mathbb {Z}}[x]$$
of
......
On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions
Geometric and Functional Analysis - Tập 24 - Trang 946-958 - 2014
We prove that the set of exceptional
$${\lambda\in (1/2,1)}$$
such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convolutions, with the exceptional set independent of the bia......
On the Dimension of Kakeya Sets and Related Maximal Inequalities
Geometric and Functional Analysis - Tập 9 - Trang 256-282 - 1999
((Without Abstract)).
Higher-Order Fourier Analysis Of $${\mathbb{F}_{p}^n}$$ And The Complexity Of Systems Of Linear Forms
Geometric and Functional Analysis - - 2011
Random Homeomorphisms and Fourier Expansions
Geometric and Functional Analysis - Tập 8 - Trang 1016-1042 - 1998
We prove that a random change of variable in general improves convergence properties of the Fourier expansions, and we give a precise quantitative estimate of the phenomenon.
K-theoretic invariants for Floer homology
Geometric and Functional Analysis - Tập 12 Số 4 - Trang 810-872 - 2002
This paper defines two K-theoretic invariants, Wh 1 and Wh 2, for individual and one-parameter families of Floer chain complexes. The chain complexes are generated by intersection points of two Lagrangian submanifolds of a symplectic manifold, and the boundary maps are determined by holomorphic curves connecting pairs of intersection points. The paper proves that Wh 1 and Wh 2 do not depend on the......
Gaussian-width gradient complexity, reverse log-Sobolev inequalities and nonlinear large deviations
Geometric and Functional Analysis - - 2018
We prove structure theorems for measures on the discrete cube and on Gaussian space, which provide sufficient conditions for mean-field behavior. These conditions rely on a new notion of complexity for such measures, namely the Gaussian-width of the gradient of the log-density. On the cube {−1, 1}n, we show that a measure
......
The Patterson–Sullivan Embedding and Minimal Volume Entropy for Outer Space
Geometric and Functional Analysis - Tập 17 - Trang 1201-1236 - 2007
Motivated by Bonahon’s result for hyperbolic surfaces, we construct an analogue of the Patterson–Sullivan–Bowen–Margulis map from the Culler–Vogtmann outer space CV (F
k
) into the space of projectivized geodesic currents on a free group. We prove that this map is a continuous embedding and thus obtain a new compactification of the......
Tổng số: 949
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