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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
 
Edited by: Pascal Auscher Université Paris-Sud, Orsay, France
Thierry Coulhon Université de Cergy-Pontoise, Cergy Pontoise, France
Alexander Grigor’yan Imperial College London, London, UK
Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
Softcover ISBN:  978-0-8218-3383-4
Product Code:  CONM/338
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7928-3
Product Code:  CONM/338.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3383-4
eBook: ISBN:  978-0-8218-7928-3
Product Code:  CONM/338.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces
Edited by: Pascal Auscher Université Paris-Sud, Orsay, France
Thierry Coulhon Université de Cergy-Pontoise, Cergy Pontoise, France
Alexander Grigor’yan Imperial College London, London, UK
Softcover ISBN:  978-0-8218-3383-4
Product Code:  CONM/338
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
eBook ISBN:  978-0-8218-7928-3
Product Code:  CONM/338.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Softcover ISBN:  978-0-8218-3383-4
eBook ISBN:  978-0-8218-7928-3
Product Code:  CONM/338.B
List Price: $255.00 $192.50
MAA Member Price: $229.50 $173.25
AMS Member Price: $204.00 $154.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3382003; 424 pp
    MSC: Primary 58; 60; 47; 53; 35;

    This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and \(p\)-Laplace operators, heat kernel and spherical inversion on \(SL_2(C)\), random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs.

    This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

    Readership

    Graduate students and research mathematicians interested in random processes and analysis on manifolds.

  • Table of Contents
     
     
    • Articles
    • Pascal Auscher — Some questions on elliptic operators [ MR 2039949 ]
    • Martin T. Barlow — Heat kernels and sets with fractal structure [ MR 2039950 ]
    • Alexander Bendikov and Laurent Saloff-Coste — Brownian motions on compact groups of infinite dimension [ MR 2039951 ]
    • Thierry Coulhon — Heat kernel and isoperimetry on non-compact Riemannian manifolds [ MR 2039952 ]
    • Bruce K. Driver — Heat kernels measures and infinite dimensional analysis [ MR 2039953 ]
    • Alexander Grigor’yan — Heat kernels and function theory on metric measure spaces [ MR 2039954 ]
    • Piotr Hajłasz — Sobolev spaces on metric-measure spaces [ MR 2039955 ]
    • Ilkka Holopainen — Quasiregular mappings and the $p$-Laplace operator [ MR 2039956 ]
    • Jay Jorgenson and Serge Lang — Spherical inversion on ${\rm SL}_2(\mathbf {C})$ [ MR 2039957 ]
    • Motoko Kotani and Toshikazu Sunada — Spectral geometry of crystal lattices [ MR 2039958 ]
    • Vladimir Maz′ya — Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces [ MR 2039959 ]
    • Stephen Semmes — Some topics related to analysis on metric spaces
    • Karl-Theodor Sturm — Probability measures on metric spaces of nonpositive curvature [ MR 2039961 ]
    • Wolfgang Woess — Generating function techniques for random walks on graphs [ MR 2039962 ]
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 3382003; 424 pp
MSC: Primary 58; 60; 47; 53; 35;

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and \(p\)-Laplace operators, heat kernel and spherical inversion on \(SL_2(C)\), random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs.

This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Readership

Graduate students and research mathematicians interested in random processes and analysis on manifolds.

  • Articles
  • Pascal Auscher — Some questions on elliptic operators [ MR 2039949 ]
  • Martin T. Barlow — Heat kernels and sets with fractal structure [ MR 2039950 ]
  • Alexander Bendikov and Laurent Saloff-Coste — Brownian motions on compact groups of infinite dimension [ MR 2039951 ]
  • Thierry Coulhon — Heat kernel and isoperimetry on non-compact Riemannian manifolds [ MR 2039952 ]
  • Bruce K. Driver — Heat kernels measures and infinite dimensional analysis [ MR 2039953 ]
  • Alexander Grigor’yan — Heat kernels and function theory on metric measure spaces [ MR 2039954 ]
  • Piotr Hajłasz — Sobolev spaces on metric-measure spaces [ MR 2039955 ]
  • Ilkka Holopainen — Quasiregular mappings and the $p$-Laplace operator [ MR 2039956 ]
  • Jay Jorgenson and Serge Lang — Spherical inversion on ${\rm SL}_2(\mathbf {C})$ [ MR 2039957 ]
  • Motoko Kotani and Toshikazu Sunada — Spectral geometry of crystal lattices [ MR 2039958 ]
  • Vladimir Maz′ya — Lectures on isoperimetric and isocapacitary inequalities in the theory of Sobolev spaces [ MR 2039959 ]
  • Stephen Semmes — Some topics related to analysis on metric spaces
  • Karl-Theodor Sturm — Probability measures on metric spaces of nonpositive curvature [ MR 2039961 ]
  • Wolfgang Woess — Generating function techniques for random walks on graphs [ MR 2039962 ]
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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