No photo of Bruce Kleiner

Bruce Kleiner

Professor of Mathematics

    1989 …2019
    If you made any changes in Pure, your changes will be visible here soon.

    Research Output 1989 2019

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