Cheeger, Jeff
Overview
Works:  36 works in 114 publications in 4 languages and 1,439 library holdings 

Genres:  Filmed lectures Nonfiction films Academic theses Conference papers and proceedings 
Roles:  Author, Editor, Honoree, Contributor, Dedicatee, Other 
Publication Timeline
.
Most widely held works about
Jeff Cheeger
 Metric and differential geometry : the Jeff Cheeger anniversary volume by Xianzhe Dai( Book )
 Applications of Cheeger's constant to the convergence rate of Markov chains on Rn by Wai Kong Yuen( Book )
 Cheeger, Jeff : Differential Geometry( )
Most widely held works by
Jeff Cheeger
Comparison theorems in riemannian geometry by
Jeff Cheeger(
Book
)
29 editions published between 1975 and 2008 in 4 languages and held by 483 WorldCat member libraries worldwide
29 editions published between 1975 and 2008 in 4 languages and held by 483 WorldCat member libraries worldwide
Geometric topology : recent developments : lectures given on the 1st session of the Centro internazionale matematico estivo
(C.I.M.E.) held at Montecatini Terme, Italy, June 412, 1990 by
Jeff Cheeger(
Book
)
20 editions published between 1990 and 1991 in English and Undetermined and held by 303 WorldCat member libraries worldwide
Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex, algebraic etc.) one can impose on a topological manifold. At the C.I.M.E. session in Montecatini, in 1990, three courses of lectures were given onrecent developments in this subject which is nowadays emerging as one of themost fascinating and promising fields of contemporary mathematics. The notesof these courses are collected in this volume and can be described as: 1) the geometry and the rigidity of discrete subgroups in Lie groups especially in the case of lattices in semisimple groups; 2) the study of the critical points of the distance function and its appication to the understanding of the topology of Riemannian manifolds; 3) the theory of moduli space of instantons as a tool for studying the geometry of lowdimensional manifolds. CONTENTS: J. Cheeger: Critical Points of Distance Functions and Applications to Geometry. M. Gromov, P. Pansu, Rigidity of Lattices: An Introduction. Chr. Okonek: Instanton Invariants and Algebraic Surfaces
20 editions published between 1990 and 1991 in English and Undetermined and held by 303 WorldCat member libraries worldwide
Geometric Topology can be defined to be the investigation of global properties of a further structure (e.g. differentiable, Riemannian, complex, algebraic etc.) one can impose on a topological manifold. At the C.I.M.E. session in Montecatini, in 1990, three courses of lectures were given onrecent developments in this subject which is nowadays emerging as one of themost fascinating and promising fields of contemporary mathematics. The notesof these courses are collected in this volume and can be described as: 1) the geometry and the rigidity of discrete subgroups in Lie groups especially in the case of lattices in semisimple groups; 2) the study of the critical points of the distance function and its appication to the understanding of the topology of Riemannian manifolds; 3) the theory of moduli space of instantons as a tool for studying the geometry of lowdimensional manifolds. CONTENTS: J. Cheeger: Critical Points of Distance Functions and Applications to Geometry. M. Gromov, P. Pansu, Rigidity of Lattices: An Introduction. Chr. Okonek: Instanton Invariants and Algebraic Surfaces
Metric and comparison geometry(
Book
)
5 editions published in 2007 in English and held by 145 WorldCat member libraries worldwide
5 editions published in 2007 in English and held by 145 WorldCat member libraries worldwide
Geometric Topology: Recent Developments : Lectures given on the 1st Session of the Centro Internazionale Matematico Estivo
(C.I.M.E.) held at Montecatini Terme, Italy, June 412, 1990 by
Jeff Cheeger(
)
1 edition published in 1991 in English and held by 31 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 31 WorldCat member libraries worldwide
Degeneration of Riemannian metrics under Ricci curvature bounds by
Jeff Cheeger(
Book
)
6 editions published in 2001 in English and Swedish and held by 29 WorldCat member libraries worldwide
6 editions published in 2001 in English and Swedish and held by 29 WorldCat member libraries worldwide
Metric and differential geometry : the Jeff Cheeger anniversary volume by
Xianzhe Dai(
Book
)
7 editions published in 2012 in English and held by 19 WorldCat member libraries worldwide
Annotation. This volume covers a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kahler geometry, index theory, hypoelliptic Laplacian and analytic torsion. It offers the most recent advances as well as surveys the new developments
7 editions published in 2012 in English and held by 19 WorldCat member libraries worldwide
Annotation. This volume covers a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kahler geometry, index theory, hypoelliptic Laplacian and analytic torsion. It offers the most recent advances as well as surveys the new developments
Surveys in differential geometry : metric and comparison geometry(
Book
)
9 editions published in 2007 in English and held by 18 WorldCat member libraries worldwide
9 editions published in 2007 in English and held by 18 WorldCat member libraries worldwide
Geometric topology recent developments ; lectures by Centro internazionale matematico estivo(
Book
)
2 editions published between 1990 and 1991 in English and held by 14 WorldCat member libraries worldwide
2 editions published between 1990 and 1991 in English and held by 14 WorldCat member libraries worldwide
Comparison theorems in Riemannian geometry by
Jeff Cheeger(
Book
)
1 edition published in 1975 in English and held by 12 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 12 WorldCat member libraries worldwide
Transgressed Euler classes of SL(2n, Z) vector bundles, adiabatic limits of eta invariants and special values of Lfunctions by
JeanMichel Bismut(
Book
)
2 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 4 WorldCat member libraries worldwide
Universal symplectic forms in the soliton theory by Fedor Soloviev(
)
1 edition published in 2010 in English and held by 4 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
1 edition published in 2010 in English and held by 4 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
[Êta]invariants and their adiabatic limits by
JeanMichel Bismut(
Book
)
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 4 WorldCat member libraries worldwide
Soft and hard symplectic geometry by
Mikhael Gromov(
Visual
)
1 edition published in 1986 in English and held by 3 WorldCat member libraries worldwide
A videotaped lecture by Mikhael Gromov on soft and hard symplectic geometry
1 edition published in 1986 in English and held by 3 WorldCat member libraries worldwide
A videotaped lecture by Mikhael Gromov on soft and hard symplectic geometry
Geometric topology : recent developments : lectures given on the 1st session of the Centro internazionale matematico estivo
(C.I.M.E.) held at Montecatini Terme, Italy ... 1990(
)
1 edition published in 1991 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 3 WorldCat member libraries worldwide
Continuity of some analytic objects under measured GromovHausdorff convergence by Yu Ding(
)
1 edition published in 2001 in English and held by 3 WorldCat member libraries worldwide
By employing similar ideas, as well as a socalled three annulus argument, we prove an intrinsic generalization of Almgren's "monotonicity of the frequency" for harmonic functions. Using this, we show that if the Ricci curvature of a Riemannian manifold Mn is almost nonnegative, and a geodesic ball BL(n)(p) & sub; Mn has almost maximal volume, then there is a harmonic coordinate system on B1(p) where L(n) depends only on n
1 edition published in 2001 in English and held by 3 WorldCat member libraries worldwide
By employing similar ideas, as well as a socalled three annulus argument, we prove an intrinsic generalization of Almgren's "monotonicity of the frequency" for harmonic functions. Using this, we show that if the Ricci curvature of a Riemannian manifold Mn is almost nonnegative, and a geodesic ball BL(n)(p) & sub; Mn has almost maximal volume, then there is a harmonic coordinate system on B1(p) where L(n) depends only on n
Collapsing Riemannian manifolds while keeping their curvature bounded by
Jeff Cheeger(
Book
)
2 editions published in 1985 in Undetermined and English and held by 3 WorldCat member libraries worldwide
2 editions published in 1985 in Undetermined and English and held by 3 WorldCat member libraries worldwide
Infinitesimal isometries and pomtryagin numbers by
Paul Frank Baum(
Book
)
1 edition published in 1966 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 3 WorldCat member libraries worldwide
Comparison and finiteness theorems for Riemannian manifolds by
Jeff Cheeger(
)
3 editions published between 1967 and 1985 in English and held by 3 WorldCat member libraries worldwide
3 editions published between 1967 and 1985 in English and held by 3 WorldCat member libraries worldwide
Comparison Theorems in Riemannian Geometry by
Jeff Cheeger(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theoremthe first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 69 deal with many of the most re
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theoremthe first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 69 deal with many of the most re
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Related Identities
 Ebin, D. G.
 Tricerri, F. (Franco) 1947 Other Editor
 De Bartolomeis, P. (Paolo) Other Editor
 Centro internazionale matematico estivo Other
 Grove, Karsten Editor
 American Mathematical Society Editor
 Dai, Xianzhe Editor Contributor
 Rong, Xiaochun Editor Contributor
 Gromov, Mikhail Author
 Okonek, Christian
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Associated Subjects
Canada Cell aggregationMathematics Differential topology Distance geometry Generalized spaces Geometry Geometry, Differential Geometry, Riemannian Global differential geometry Index theory (Mathematics) Ktheory Lie groups Markov processes Mathematicians Mathematics Riemannian manifolds Scientists Stochastic processes Symplectic manifolds United States
Alternative Names
Cheeger, J.
Cheeger, J. 1943
Cheeger, J. (Jeff)
Cheeger, Jeffrey.
Cheeger, Jeffrey 1943
Jeff Cheeger Amerikaans wiskundige
Jeff Cheeger amerikansk matematikar
Jeff Cheeger amerikansk matematiker
Jeff Cheeger matemático estadounidense
Jeff Cheeger matematico statunitense
Jeff Cheeger Mathématicien américain
Jeff Cheeger USamerikanischer Mathematiker
Jeff Cheeger usona matematikisto
제프 치거
ジェフ・チーガー
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