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Bruce Kleiner

Professor of Mathematics

1989 …2019
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Research Output 1989 2019

  • 65 Article
  • 2 Conference contribution
  • 1 Chapter
  • 1 Chapter (peer-reviewed)
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Article
2019

Rectifiability of planes and Alberti representations

David, G. C. & Kleiner, B., Jan 1 2019, In : Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 19, 2, p. 723-756 34 p.

Research output: Contribution to journalArticle

Rectifiability
Metric Measure Space
Doubling
Differentiable
Restriction
2018

Groups quasi-isometric to right-angled Artin groups

Huang, J. & Kleiner, B., Feb 1 2018, In : Duke Mathematical Journal. 167, 3, p. 537-602 66 p.

Research output: Contribution to journalArticle

Right-angled Artin Group
Quasigroup
Isometric
Outer Automorphism Groups
Equivariant
2017

Mean curvature flow with surgery

Haslhofer, R. & Kleiner, B., 2017, In : Duke Mathematical Journal. 166, 9, p. 1591-1626 36 p.

Research output: Contribution to journalArticle

Mean Curvature Flow
Surgery
Convex Surface
A Priori Estimates
Hypersurface

Singular Ricci flows I

Kleiner, B. & Lott, J., Sep 1 2017, In : Acta Mathematica. 219, 1, p. 65-134 70 p.

Research output: Contribution to journalArticle

Ricci Flow
Surgery
Initial conditions
Space-time
Singularity
2016

Differentiable structures on metric measure spaces: A primer

Kleiner, B. & Mackay, J. M., 2016, In : Annali della Scuola Normale - Classe di Scienze. 16, 1, p. 41-64 24 p.

Research output: Contribution to journalArticle

Metric Measure Space
Differentiable

Infinitesimal Structure of Differentiability Spaces, and Metric Differentiation

Cheeger, J., Kleiner, B. & Schioppa, A., 2016, In : Analysis and Geometry in Metric Spaces. 4, 1, p. 104-159 56 p.

Research output: Contribution to journalArticle

Differentiability
Metric

Mean Curvature Flow of Mean Convex Hypersurfaces

Haslhofer, R. & Kleiner, B., 2016, (Accepted/In press) In : Communications on Pure and Applied Mathematics.

Research output: Contribution to journalArticle

Mean Curvature Flow
Surgery
Hypersurface
Derivatives
Estimate

Quasiflats in CAT(0) 2-complexes

Bestvina, M., Kleiner, B. & Sageev, M., Nov 7 2016, In : Algebraic and Geometric Topology. 16, 5, p. 2663-2676 14 p.

Research output: Contribution to journalArticle

CAT(0)
Isometry Group
Hausdorff Distance
Compact Set
Euclidean
2015

Infinitesimal structure of differentiability spaces and metric differentiation

Cheeger, J., Kleiner, B. & Schioppa, A., 2015, In : arXiv:1503.0734.

Research output: Contribution to journalArticle

Inverse limit spaces satisfying a poincaré inequality

Cheeger, J. & Kleiner, B., 2015, In : Analysis and Geometry in Metric Spaces. 3, 1, p. 15-39 25 p.

Research output: Contribution to journalArticle

Inverse Limit Space
Radon
Banach spaces
Radon-Nikodym Property
Inverse System

Inverse limit spaces satisfying poincare inequality

Cheeger, J. & Kleiner, B., 2015, In : Analysis and Geometry in Metric Spaces. 3, p. 15-39

Research output: Contribution to journalArticle

On Brendle's Estimate for the Inscribed Radius under Mean Curvature Flow

Haslhofer, R. & Kleiner, B., 2015, In : International Mathematics Research Notices. 2015, 15, p. 6558-6561 4 p.

Research output: Contribution to journalArticle

Mean Curvature Flow
Radius
Estimate
Hypersurface
Closed

Some applications of ℓ<inf>p</inf>-cohomology to boundaries of Gromov hyperbolic spaces

Bourdon, M. & Kleiner, B., 2015, In : Groups, Geometry, and Dynamics. 9, 2, p. 435-478 44 p.

Research output: Contribution to journalArticle

Hyperbolic Space
Cohomology
Hyperbolic Groups
Quasi-isometry
Sierpinski Carpet
2014

Geometrization of three-dimensional orbifolds via Ricci flow

Kleiner, B. & Lott, J., 2014, In : Asterisque. 365, p. 101-177 77 p.

Research output: Contribution to journalArticle

Ricci Flow
Orbifold
Three-dimensional
Decompose
Closed

Locally collapsed 3-manifolds

Kleiner, B. & Lott, J., 2014, In : Asterisque. 365, p. 7-99 93 p.

Research output: Contribution to journalArticle

Compact Manifold
Riemannian Manifold
Curvature
Graph in graph theory
Theorem
2013

Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups

Bourdon, M. & Kleiner, B., 2013, In : Groups, Geometry, and Dynamics. 7, 1, p. 39-107 69 p.

Research output: Contribution to journalArticle

Coxeter Group
Modulus
Hyperbolic Groups
Metric space
Cohomology

Realization of Metric Spaces as Inverse Limits, and Bilipschitz Embedding in L1

Cheeger, J. & Kleiner, B., 2013, In : Geometric and Functional Analysis. 23, 1, p. 96-133 38 p.

Research output: Contribution to journalArticle

Inverse Limit
Metric space
Embedding Theorem
Lipschitz Map
Metric Graphs
2012

Geometry and rigidity of mapping class groups

Behrstock, J., Kleiner, B., Minsky, Y. & Mosher, L., 2012, In : Geometry and Topology. 16, 2, p. 781-888 108 p.

Research output: Contribution to journalArticle

Curve Complex
Mapping Class Group
Isometric
Rigidity
Asymptotic Cone
2011

Compression bounds for Lipschitz maps from the Heisenberg group to L 1

Cheeger, J., Kleiner, B. & Naor, A., Dec 2011, In : Acta Mathematica. 207, 2, p. 291-373 83 p.

Research output: Contribution to journalArticle

Lipschitz Map
Semidefinite Relaxation
Integrality
Heisenberg Group
Lipschitz
2010

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

Kleiner, B., Jul 2010, In : Journal of the American Mathematical Society. 23, 3, p. 815-829 15 p.

Research output: Contribution to journalArticle

Polynomial Growth
Polynomials
Theorem

Differentiating maps into L1, and the geometry of BV functions

Cheeger, J. & Kleiner, B., 2010, In : Annals of Mathematics. 171, 2, p. 1347-1385 39 p.

Research output: Contribution to journalArticle

BV Functions
Lipschitz Map
Heisenberg Group
Differentiability
Lipschitz

Metric differentiation, monotonicity and maps to L1

Cheeger, J. & Kleiner, B., 2010, In : Inventiones Mathematicae. 182, 2, p. 335-370 36 p.

Research output: Contribution to journalArticle

Lipschitz Map
Heisenberg Group
Monotonicity
Metric
Theorem
2009
Lipschitz Map
Radon-Nikodym Property
Metric Measure Space
Differentiability
Banach space

Erratum to: Hadamard spaces with isolated flats [Geometry and Topology 9 (2005), 1501-1538]

Hruska, G. C. & Kleiner, B., 2009, In : Geometry and Topology. 13, 2, p. 699-707

Research output: Contribution to journalArticle

Induced quasi-actions: A remark

Kleiner, B. & Leeb, B., May 2009, In : Proceedings of the American Mathematical Society. 137, 5, p. 1561-1567 7 p.

Research output: Contribution to journalArticle

Induced Representations
Analogue

Lacunary hyperbolic groups

Ol'shanskii, A. Y., Osin, D. V., Sapir, M. V., Kapovich, M. & Kleiner, B., 2009, In : Geometry and Topology. 13, 4, p. 2051-2140 90 p.

Research output: Contribution to journalArticle

Hyperbolic Groups
Asymptotic Cone
Finitely Generated Group
Torsion
Direct Limit

Rectifiability of sets of finite perimeter in carnot groups: Existence of a tangent hyperplane

Ambrosio, L., Kleiner, B. & Le Donne, E., 2009, In : Journal of Geometric Analysis. 19, 3, p. 509-540 32 p.

Research output: Contribution to journalArticle

Rectifiability
Carnot Group
Perimeter
Hyperplane
Tangent line

Rigidity of schottky sets

Bonk, M., Kleiner, B. & Merenkov, S., 2009, In : American Journal of Mathematics. 131, 2, p. 409-443 35 p.

Research output: Contribution to journalArticle

Rigidity
Totally Geodesic
Hyperbolic Space
Homeomorphism
Unit Sphere
2008

Notes on Perelman's papers

Kleiner, B. & Lott, J., 2008, In : Geometry and Topology. 12, 5, p. 2587-2855 269 p.

Research output: Contribution to journalArticle

Ricci Flow
Three-manifolds
Surgery
Entropy

The asymptotic geometry of rightangled Artin groups, I

Bestvina, M., Kleiner, B. & Sageev, M., 2008, In : Geometry and Topology. 12, 3, p. 1653-1699 47 p.

Research output: Contribution to journalArticle

Artin Groups
Right-angled Artin Group
Isometric
Rigidity
Deduce
2007

The weak hyperbolization conjecture for 3-dimensional CAT(0)-groups

Kapovich, M. & Kleiner, B., 2007, In : Groups, Geometry, and Dynamics. 1, 1, p. 61-79

Research output: Contribution to journalArticle

2006

Generalized differentiation and bi-Lipschitz nonembedding in L1

Cheeger, J. & Kleiner, B., Sep 1 2006, In : Comptes Rendus Mathematique. 343, 5, p. 297-301 5 p.

Research output: Contribution to journalArticle

Generalized Differentiation
Lipschitz
Heisenberg Group
Differentiability
Lipschitz Mapping

Rigidity of invariant convex sets in symmetric spaces

Kleiner, B. & Leeb, B., Mar 2006, In : Inventiones Mathematicae. 163, 3, p. 657-676 20 p.

Research output: Contribution to journalArticle

Invariant Set
Symmetric Spaces
Convex Sets
Rigidity
Imply
2005

Coarse Alexander duality and duality groups

Kapovich, M. & Kleiner, B., Feb 2005, In : Journal of Differential Geometry. 69, 2, p. 279-352 74 p.

Research output: Contribution to journalArticle

Alexander Duality
Duality
Group Action
Subgroup
Quasi-isometry

Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary

Bonk, M. & Kleiner, B., Jan 26 2005, In : Geometry and Topology. 9, p. 219-246 28 p.

Research output: Contribution to journalArticle

Hyperbolic Groups
Homeomorphic
Metric

Hadamard spaces with isolated flats

Hruska, G. C., Kleiner, B. & Hindawi, M., Aug 8 2005, In : Geometry and Topology. 9

Research output: Contribution to journalArticle

CAT(0) Spaces
Homeomorphism
Equivariant
Euclidean
Disjoint

Quasi-hyperbolic planes in hyperbolic groups

Bonk, M. & Kleiner, B., Sep 2005, In : Proceedings of the American Mathematical Society. 133, 9, p. 2491-2494 4 p.

Research output: Contribution to journalArticle

Isometric Embedding
Hyperbolic Groups
Hyperbolic Plane
2004

Rigidity for quasi-fuchsian actions on negatively curved spaces

Bonk, M. & Kleiner, B., 2004, In : International Mathematics Research Notices. 61, p. 3309-3316 8 p.

Research output: Contribution to journalArticle

Rigidity
2003

Singularity structure in mean curvature flow of mean-convex sets

Colding, T. H. & Kleiner, B., 2003, In : Electronic Research Announcements of the American Mathematical Society. 9, p. 121-124 4 p.

Research output: Contribution to journalArticle

Mean Curvature Flow
Convex Sets
Singularity
Justify
Three-dimension
2002

Quasisymmetric parametrizations of two-dimensional metric spheres

Bonk, M. & Kleiner, B., 2002, In : Inventiones Mathematicae. 150, 1, p. 127-183 57 p.

Research output: Contribution to journalArticle

Parametrization
Metric

Rectifying separated nets

Burago, D. & Kleiner, B., 2002, In : Geometric and Functional Analysis. 12, 1, p. 80-92 13 p.

Research output: Contribution to journalArticle

Rigidity for quasi-möbius group actions

Bonk, M. & Kleiner, B., Jan 1 2002, In : Journal of Differential Geometry. 61, 1, p. 81-106 26 p.

Research output: Contribution to journalArticle

Quasigroup
Group Action
Rigidity
Distinct

Rigidity for quasi-Mobus group actions

Bonk, M. & Kleiner, B., 2002, In : Journal of Differential Geometry. 61, 1, p. 81-106

Research output: Contribution to journalArticle

The geodesic flow of a nonpositively curved graph manifold

Croke, C. B. & Kleiner, B., 2002, In : Geometric and Functional Analysis. 12, 3, p. 479-545 67 p.

Research output: Contribution to journalArticle

Geodesic Flow
Graph in graph theory
Equivariant
Geodesic
Half line

Van Kampen's embedding obstruction for discrete groups

Bestvina, M., Kapovich, M. & Kleiner, B., 2002, In : Inventiones Mathematicae. 150, 2, p. 219-235 17 p.

Research output: Contribution to journalArticle

Discrete Group
Free Group
Obstruction
Fold
Lower bound
2001

Gluing copies of a 3-dimensional polyhedron to obtain a closed nonpositively curved pseud omanifold

Burago, D., Ferleger, S., Kleiner, B. & Kononenko, A., 2001, In : Proceedings of the American Mathematical Society. 129, 5, p. 1493-1498 6 p.

Research output: Contribution to journalArticle

Gluing
Glues
Polyhedron
Closed
Riemannian Manifold

Groups quasi-isometric to symmetric spaces

Kleiner, B. & Leeb, B., Apr 2001, In : Communications in Analysis and Geometry. 9, 2, p. 239-260 22 p.

Research output: Contribution to journalArticle

Quasigroup
Finitely Generated Group
Symmetric Spaces
Isometric
Euclidean
2000

Hyperbolic groups with low-dimensional boundary

Kapovich, M. & Kleiner, B., Sep 2000, In : Annales Scientifiques de l'Ecole Normale Superieure. 33, 5, p. 647-669 23 p.

Research output: Contribution to journalArticle

Sierpinski Carpet
Hyperbolic Groups
Torsion-free Group
Quasiconvex
Cyclic group

Spaces with nonpositive curvature and their ideal boundaries

Croke, C. B. & Kleiner, B., May 2000, In : Topology. 39, 3, p. 549-556 8 p.

Research output: Contribution to journalArticle

Nonpositive Curvature
Universal Cover
Homeomorphic
Euclidean
1999

The local structure of length spaces with curvature bounded above

Kleiner, B., Jul 1999, In : Mathematische Zeitschrift. 231, 3, p. 409-456 48 p.

Research output: Contribution to journalArticle

Local Structure
Curvature
Asymptotic Cone
CAT(0) Spaces
Isometry Group