Bruce Kleiner

Rigidity of Schottky sets (2009)

We give a new approach to the infinitesimal structure of Lipschitz maps into L^1. As a first application, we give an alternative proof of the main theorem from an earlier paper, that the Heisenberg...

Mario Bonk, Bruce Kleiner, Sergei Merenkov

Dedicated to the memory of Juha Heinonen. Abstract. We call a complement of a union of at least three disjoint (round) open balls in the unit sphere S n a Schottky set. We prove that every...

Rigidity of Schottky sets (2009)

Mario Bonk, Bruce Kleiner, Sergei Merenkov

American Journal of Mathematics - Volume 131, Number 2, April 2009

CHARACTERIZATION OF THE RADON-NIKODYM PROPERTY IN TERMS OF INVERSE LIMITS (2009)

Rigidity of Schottky sets (2008)

Abstract. In this paper we clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho [JH81], and the GFDA spaces introduced in

Mario Bonk, Bruce Kleiner, Sergei Merenkov

Abstract. We call a complement of a union of at least three disjoint open balls in the unit sphere S n a Schottky set. We prove that every quasisymmetric homeomorphism of a Schottky set of spherical...

INDUCED QUASI-ACTIONS: A REMARK (2008)

A NEW PROOF OF GROMOV’S THEOREM ON GROUPS OF POLYNOMIAL GROWTH (2008)

In this note we observe that the notion of an induced representation has an analog for quasi-actions, and give some applications. We will use the definitions and notation from [KL01]. 1.1. Induced...

Bruce Kleiner

Abstract. We give a proof of Gromov’s theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. The proof does not rely on the Montgomery-Zippin-Yamabe...

Erratum on "Hadamard spaces with isolated flats" (2008)

Hruska, G. Christopher, Kleiner, Bruce

The purpose of this erratum is to correct the proof of Theorem A.0.1 in the appendix to our article ``Hadamard spaces with isolated flats'' math.GR/0411232, which was jointly authored by Mohamad...

Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property (2008)

THE WEAK HYPERBOLIZATION CONJECTURE FOR 3-DIMENSIONAL CAT(0) GROUPS (2008)

We prove the differentiability of Lipschitz maps X-->V, where X is a complete metric measure space satisfying a doubling condition and a Poincar\'e inequality, and V is a Banach space with the Radon...

Abstract. We prove a weak hyperbolization conjecture for CAT(0) 3-dimensional Poincaré duality groups. 1.

Contents (2008)

Quasiflats in CAT(0) complexes (2008)

Abstract. This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X → V, and bi-Lipschitz nonembeddability, where X is a metric measure space...

Bestvina, Mladen, Kleiner, Bruce, Sageev, Michah

We show that if X is a piecewise Euclidean 2-complex with a cocompact isometry group, then every 2-quasiflat in X is at finite Hausdorff distance from a subset which is locally flat outside a compact...

Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane (2008)

Ambrosio, Luigi, Kleiner, Bruce, Donne, Enrico Le

We consider sets of locally finite perimeter in Carnot groups. We show that if E is a set of locally finite perimeter in a Carnot group G, then for almost every x in G with respect to the perimeter...

Induced quasi-actions: a remark (2008)

Geometry and rigidity of mapping class groups (2008)

In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.

Behrstock, Jason, Kleiner, Bruce, Minsky, Yair, Mosher, Lee

We study the large scale geometry of mapping class groups MCG(S), using hyperbolicity properties of curve complexes. We show that any self quasi-isometry of MCG(S) (outside a few sporadic cases) is a...

\Gamma1 (2007)

Hyperbolic groups with low-dimensional boundary (2007)

Abstract. We study quasi-isometries between products of symmetric spaces and Euclidean buildings. The main results are that quasi-isometries preserve product structure, and in the irreducible higher...

Michael Kapovich, Bruce Kleiner, Bernhard Leeb

If a torsion-free hyperbolic group G has 1-dimensional boundary @1G, then @1G is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When

y (2007)

We study quasi-isometries \Phi: Q

Spaces (2007)

Christopher B. Croke, Bruce Kleiner

with nonpositive curvature and their ideal boundaries

Groups quasi-isometric to symmetric spaces (2007)

A new proof of Gromov's theorem on groups of polynomial growth (2007)

We determine the structure of finitely generated groups which are quasi-isometric to symmetric spaces of noncompact type, allowing Euclidean de Rham factors. If X is a symmetric space of noncompact...

bounded (2007)

Bruce Kleiner

local structure of length spaces with curvature

Kleiner, Bruce

We give a new proof of Gromov's theorem that any finitely generated group of polynomial growth has a finite index nilpotent subgroup. Unlike the original proof, it does not rely on the...

The asymptotic geometry of right-angled Artin groups, I (2007)

Bestvina, Mladen, Kleiner, Bruce, Sageev, Michah

We study atomic right-angled Artin groups -- those whose defining graph has no cycles of length less than five, and no separating vertices, separating edges, or separating vertex stars. We show that...

Characterization of the Radon-Nikodym Property in terms of inverse limits (2007)

Differentiating maps into L^1 and the geometry of BV functions (2006)

We clarify the relation between inverse systems, the Radon-Nikodym property, the Asymptotic Norming Property of James-Ho, and the GFDA spaces introduced in our earlier paper on differentiability of...

Notes on Perelman's papers (2006)

This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X-->V, and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a...

Kleiner, Bruce, Lott, John

These are detailed notes on Perelman's papers "The entropy formula for the Ricci flow and its geometric applications" and "Ricci flow with surgery on three-manifolds".

Rigidity of invariant convex sets in symmetric spaces (2006)

The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity (2006)

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.

Bruce Kleiner

On the differentiation of Lipschitz maps from metric measure spaces to Banach spaces (2006)

Generalized differentiation and bi-Lipschitz nonembedding (2006)

Abstract. We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real...

Coarse Alexander duality and duality groups (2005)

Résumé. We consider Lipschitz mappings f: X → V, where X is a doubling metric measure space which satisfies a Poincaré inequality, and V is a Banach space. We show that earlier differentiability...

Coarse Alexander duality and duality groups (2005)

We study discrete group actions on coarse Poincaré duality spaces, e.g., acyclic simplicial complexes which admit free cocompact group actions by Poincaré duality groups. When G is an (n−1)...

Rigidity of invariant convex sets in symmetric spaces (2004)

Hadamard spaces with isolated flats (2004)

The main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have Zariski dense stabilizer.

Hruska, G Christopher, Kleiner, Bruce

We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces. We prove...

Geometry of quasi-planes (2004)

Rigidity for quasi-Fuchsian actions on negatively curved spaces (2004)

Abstract. In this paper we discuss metric cell complexes satisfying a coarse form of 2-dimensional Poincaré duality. We prove that such spaces are either Gromov-hyperbolic or have polynomial growth....

Singularity structure in mean curvature flow of mean convex sets (2003)

We prove that if $$G\curvearrowright X$$ is a convex cocompact isometric group action on a CAT(−1) space, and the limit set has Hausdorff and topological dimensions equal to 1, then the action...

Colding, Tobias H., Kleiner, Bruce

In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only...

Quasi-hyperbolic planes in hyperbolic groups (2003)

Van Kampen’s embedding obstruction for discrete groups (2002)

The hyperbolic plane admits a quasi-isometric embedding into a hyperbolic group if and only if the group is not virtually free.

Kleiner, Bruce, Bestvina, Mladen, Kapovich, Michael

We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously. In particular, we show that the n -fold product of nonabelian free groups...

Quasisymmetric parametrizations of two-dimensional metric spheres (2002)

Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary (2002)

Peer Reviewed

Rigidity for Quasi-Möbius Group Actions (2002)

Suppose G is a Gromov hyperbolic group, and the boundary at infinity of G is quasisymmetrically homeomorphic to an Ahlfors Q-regular metric 2-sphere Z with Ahlfors regular conformal dimension Q. Then...

Rectifying separated nets (2002)

If a group acts by uniformly quasi-Möbius homeomorphisms on a compact Ahlfors n-regular space of topological dimension n such that the induced action on the space of distinct triples is cocompact,...

Kleiner, Bruce, Burago, D.

((Without Abstract)).

Quasisymmetric parametrizations of two-dimensional metric spheres (2001)

Van Kampen's embedding obstruction for discrete groups (2000)

We study metric spaces homeomorphic to the 2-sphere, and find conditions under which they are quasisymmetrically homeomorphic to the standard 2-sphere. As an application of our main theorem we show...

Bestvina, Mladen, Kapovich, Michael, Kleiner, Bruce

We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously. In particular, we show that the $n$-fold product of nonabelian free groups...

Rigidity for Quasi-Mobius group actions (2000)

Hyperbolic groups with low-dimensional boundary (2000)

Suppose G is a hyperbolic group whose boundary has topological dimension k. If the boundary is quasisymmetrically homeomorphic to an Ahlfors k-regular metric space, then, modulo a finite normal...

Van Kampen's embedding obstruction for discrete groups (2000)

Mladen Bestvina, Michael Kapovich, Bruce Kleiner

We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously. In particular, we show that the n-fold product of nonabelian free groups...

Hyperbolic Groups With Low Dimensional Boundary (2000)

The geodesic flow of a nonpositively curved graph manifold (1999)

If a torsion-free hyperbolic group G has 1-dimensional boundary @1G, then @1G is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When @1G is a Sierpinski carpet...

Croke, Christopher B., Kleiner, Bruce

We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional...

Coarse Alexander duality and duality groups (1999)

Coarse Alexander duality and duality groups, preprint (1999)

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n-1)...

Coarse Alexander duality and duality groups (1999)

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n − 1)...

Misha Kapovich, Bruce Kleiner

We study discrete group actions on coarse Poincare duality spaces, e.g. acyclic simplicial complexes which admit free cocompact group actions by Poincare duality groups. When G is an (n \Gamma 1)...

Hyperbolic groups with 1-dimensional boundary (1998)

Separated nets in euclidean space and jacobians of bi-lipschitz maps (1998)

If a torsion-free hyperbolic group G has 1-dimensional boundary, then the boundary is a Menger curve or a Sierpinski carpet provided G does not split over a cyclic group. When the boundary of G is a...

Dimtri Burago, Bruce Kleiner

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is...

Separated nets in Euclidean space and Jacobians of biLipschitz maps (1997)

Burago, Dmitri, Kleiner, Bruce

We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is...

Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings (1997)

Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings (1997)

Separated Nets In Euclidean Space And Jacobians Of Bilipschitz Maps (1997)

1.1 Background and statement of results An (L, C) quasi-isometry is a map Φ: X − → X ′ between metric spaces such that for all x1, x2 ∈ X

Dimtri Burago, BRUCE KLEINER

. We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is...

Groups quasi-isometric to symmetric spaces (1996)