Cheeger, Jeff
Overview
Works:  32 works in 105 publications in 5 languages and 1,405 library holdings 

Genres:  Academic theses Filmed lectures Nonfiction films Conference papers and proceedings 
Roles:  Author, Editor, Other, Dedicatee 
Classifications:  QA649, 516.92 
Publication Timeline
.
Most widely held works about
Jeff Cheeger
 Metric and differential geometry : the Jeff Cheeger anniversary volume by Xianzhe Dai( Book )
 Cheeger, Jeff : Differential Geometry( )
 Applications of Cheeger's constant to the convergence rate of Markov chains on Rn by Wai Kong Yuen( Book )
Most widely held works by
Jeff Cheeger
Comparison theorems in riemannian geometry by
Jeff Cheeger(
Book
)
30 editions published between 1975 and 2008 in 4 languages and held by 496 WorldCat member libraries worldwide
30 editions published between 1975 and 2008 in 4 languages and held by 496 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
)
19 editions published in 1991 in English and Undetermined and held by 309 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
19 editions published in 1991 in English and Undetermined and held by 309 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
)
6 editions published in 2007 in English and held by 145 WorldCat member libraries worldwide
6 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 30 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 30 WorldCat member libraries worldwide
Degeneration of Riemannian metrics under Ricci curvature bounds by
Jeff Cheeger(
Book
)
5 editions published in 2001 in English and Swedish and held by 29 WorldCat member libraries worldwide
5 editions published in 2001 in English and Swedish and held by 29 WorldCat member libraries worldwide
Surveys in differential geometry : metric and comparison geometry(
Book
)
9 editions published in 2007 in English and held by 17 WorldCat member libraries worldwide
9 editions published in 2007 in English and held by 17 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
Universal symplectic forms in the soliton theory by Fedor Soloviev(
)
1 edition published in 2010 in English and held by 8 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 8 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
Metric type and cotype in Banach spaces by Ohad Giladi(
)
1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
Rademacher type and cotype of Banach spaces are well known notions in geometric functional analysis. Originally introduced in the context of vector valued limit theorems, they proved to have numerous applications in the geometry of Banach spaces. While their original definition relies heavily on the linear structure of the space, in the last several decades a great effort has been put into finding metric characterizations of these notions. This direction of research is part of a broader program, which aims at finding metric characterization of local properties of Banach spaces (a property is called local if its definition involves only finitely many vectors). The reason why one should seek for such a characterization is a classical theorem of Ribe from the 70's, which says that all local properties are invariant under uniform homeomorphisms and therefore should be independent of the linear structure of the space. This thesis gives a description of the various metric analogues of Rademacher type and cotype, and discusses related embedding problems of metric spaces and Banach spaces
1 edition published in 2011 in English and held by 7 WorldCat member libraries worldwide
Rademacher type and cotype of Banach spaces are well known notions in geometric functional analysis. Originally introduced in the context of vector valued limit theorems, they proved to have numerous applications in the geometry of Banach spaces. While their original definition relies heavily on the linear structure of the space, in the last several decades a great effort has been put into finding metric characterizations of these notions. This direction of research is part of a broader program, which aims at finding metric characterization of local properties of Banach spaces (a property is called local if its definition involves only finitely many vectors). The reason why one should seek for such a characterization is a classical theorem of Ribe from the 70's, which says that all local properties are invariant under uniform homeomorphisms and therefore should be independent of the linear structure of the space. This thesis gives a description of the various metric analogues of Rademacher type and cotype, and discusses related embedding problems of metric spaces and Banach spaces
Continuity of some analytic objects under measured GromovHausdorff convergence by Yu Ding(
)
1 edition published in 2001 in English and held by 7 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 7 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
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
[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 4 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 4 WorldCat member libraries worldwide
A videotaped lecture by Mikhael Gromov on soft and hard symplectic geometry
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
The small scale structure of Riemannian manifolds by
Jeff Cheeger(
Visual
)
3 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2004 in 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
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
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
Analyse et topologie sur les espaces singuliers : CIRM, 610 juillet 1981 by Colloque Analyse et topologie sur les espaces singuliers(
Book
)
2 editions published between 1982 and 1983 in French and held by 2 WorldCat member libraries worldwide
2 editions published between 1982 and 1983 in French and held by 2 WorldCat member libraries worldwide
Differential geometry : a symposium in honour of Manfredo do Carmo(
Book
)
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 2 WorldCat member libraries worldwide
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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
 Dai, Xianzhe
 Rong, Xiaochun
 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 American mathematician
Jeff Cheeger Amerikaans wiskundige
Jeff Cheeger amerikansk matematikar
Jeff Cheeger amerikansk matematiker
Jeff Cheeger matemático estadounidense
Jeff Cheeger Mathématicien américain
Jeff Cheeger USamerikanischer Mathematiker
제프 치거
ジェフ・チーガー
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