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Isometric actions of Heisenberg groups on compact Lorentz manifolds
Heisenberg groupsl Lorentz manifolds
2015/10/14
We prove results toward classifying compact Lorentz manifolds on
which Heisenberg groups act isometrically. We give a general construction,
leading to a new example, of codimension-one actions—those...
Harnack inequality for fractional sub-Laplacians in Carnot groups
Carnot groups heat kernel fractional powers of sub-Laplacian Harnack inequality
2012/6/21
In this paper we prove an invariant Harnack inequality on Carnot-Carath\'eodory balls for fractional powers of sub-Laplacians in Carnot groups. The proof relies on an "abstract" formulation of a techn...
On critical cases of Sobolev's inequalities for Heisenberg groups
Heisenberg group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/17
This paper deal with the problem of Sobolev imbedding in the critical cases. We prove some Trudinger-type inequalities on the whole Heisenberg group, extending to this context the Euclidean results by...
On critical cases of Sobolev's inequalities for Carnot groups
Carnot group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/15
In this paper we deal with the problem of Sobolev imbedding in thecritical cases on Carnot groups. We prove some Trudinger-type inequalities on the whole Carnot group, extending to this context the Eu...
Two characterization of BV functions on Carnot groups via the heat semigroup
Functions of bounded variation perimeters Carnot groups Heat semigroup
2011/9/15
Abstract: In this paper we provide two different characterizations of sets with finite perimeter and functions of bounded variation in Carnot groups, analogous to those which hold in Euclidean spaces,...
On The Torsion Homology of Non-Arithmetic Hyperbolic Tetrahedral Groups
Torsion Homology Non-Arithmetic Hyperbolic Tetrahedral Groups
2011/1/19
Numerical data concerning the growth of torsion in the first homology of non-arithmetic hyperbolic tetrahedral groups are collected. The data provide support the speculations of Bergeron and Venkatesh...
Kähler groups, real hyperbolic spaces and the Cremona group
Kä hler groups real hyperbolic spaces Cremona group
2011/1/19
Generalizing a classical theorem of Carlson and Toledo, we prove that any Zariski dense isometric action of a K¨ahler group on the real hyperbolic space of dimension at least 3 factors through a homom...
Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Carnot groups Sub-Riemannian Geometry Hypersurfaces Isoperimetric Inequality
2011/1/20
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Our main result is an isoperimetric inequality for the case of a C2-smooth compact hype...
Hyperbolic surface subgroups of one-ended doubles of free groups
hyperbolic group surface group diskbusting polygonality
2010/12/9
Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group contains a hyperbolic surface
group if the free gr...
On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve
Ranks of the 2-Selmer Groups of Twists Given Elliptic Curve
2010/12/1
On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve.
Simple closed curves, word length, and nilpotent quotients of free groups
ISimple closed curves word length nilpotent quotients of free groups
2010/11/29
We consider the fundamental group p of a surface of finite type equipped with the infinite generating set consisting of all simple closed curves. We show that every nilpotent quotient of p has finite ...
Hyperboloid preservation implies the Lorentz and Poincaré groups without dilations
mass shell momentum space velocity hyperboloid proper time velocity Lorentz transformation Poincar´ e transformation
2010/12/9
An analogue of the Alexandrov-Zeeman theorem, based on hyperboloid preservation, as opposed to light cone preservation, is provided. This char-acterizes exactly the Poincar´e group, as opposed t...
Conjugacy p-separability of right-angled Artin groups and applications
Conjugacy p-separability right-angled Artin groups applications
2010/12/9
We prove that every subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. In particular, every right-angled Artin group is conjugacy p-separable. A consequence of this resu...