Geometric and Functional Analysis
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Stable Norms of Surfaces: Local Structure of the Unit Ball at Rational Directions
Geometric and Functional Analysis - Tập 7 - Trang 996-1010 - 1997
Let (M, g) be a closed orientable surface, equipped with a smooth Finsler metric. The metric induces a norm on the real homology of M, called a stable norm. We show this norm is neither strictly convex, nor smooth.
Multiple Recurrence Theorem for Measure Preserving Actions of a Nilpotent Group
Geometric and Functional Analysis - Tập 8 Số 5 - Trang 853-931 - 1998
The Cut Loci, Conjugate Loci and Poles in a Complete Riemannian Manifold
Geometric and Functional Analysis - Tập 22 - Trang 1400-1406 - 2012
Let M be a complete Riemannian manifold. We first prove that there exist at least two geodesics connecting p and every point in M if the tangent cut locus of
$${p \in M}$$
is not empty and does not meet its tangent conjugate locus. It follows from this that if M admits a pole and
......
Flattening a non-degenerate CR singular point of real codimension two
Geometric and Functional Analysis - Tập 28 - Trang 289-333 - 2018
This paper continues the previous studies in two papers of Huang–Yin [HY16,HY17] on the flattening problem of a CR singular point of real codimension two sitting in a submanifold in
$${{\mathbb {C}}^{n+1}}$$
with n + 1 ≥ 3, whose CR points are no......
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 ......
Polynomial bound for partition rank in terms of analytic rank
Geometric and Functional Analysis - Tập 29 - Trang 1503-1530 - 2019
Let
$$G_1, \ldots , G_k$$
be vector spaces over a finite field
$${\mathbb {F}} = {\mathbb {F}}_q$$
......
Constant mean curvature hypersurfaces condensing on a submanifold
Geometric and Functional Analysis - Tập 16 - Trang 924-958 - 2006
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......
Coniveau 2 Complete Intersections and Effective Cones
Geometric and Functional Analysis - Tập 19 - Trang 1494-1513 - 2009
Griffiths computation of the Hodge filtration on the cohomology of a smooth hypersurface X of degree d in
$${\mathbb{P}^n}$$
shows that it has coniveau ≥ c once n ≥ dc. The generalized Hodge conjecture (GHC) predicts that the cohomology of X is then supported on a closed algebraic subset of codimension a......
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