Handbook of Global Analysis

1st Edition

Editors: Demeter Krupka David Saunders
Hardcover ISBN: 9780444528339
eBook ISBN: 9780080556734
Imprint: Elsevier Science
Published Date: 27th November 2007
Page Count: 1244
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This is a comprehensive exposition of topics covered by the American Mathematical Society’s classification “Global Analysis”, dealing with modern developments in calculus expressed using abstract terminology. It will be invaluable for graduate students and researchers embarking on advanced studies in mathematics and mathematical physics.

This book provides a comprehensive coverage of modern global analysis and geometrical mathematical physics, dealing with topics such as; structures on manifolds, pseudogroups, Lie groupoids, and global Finsler geometry; the topology of manifolds and differentiable mappings; differential equations (including ODEs, differential systems and distributions, and spectral theory); variational theory on manifolds, with applications to physics; function spaces on manifolds; jets, natural bundles and generalizations; and non-commutative geometry.

Key Features

  • Comprehensive coverage of modern global analysis and geometrical mathematical physics
  • Written by world-experts in the field
  • Up-to-date contents


This book is suitable for university mathematics departments, libraries and students in mathematics and mathematical physics.

Table of Contents

Preface Contents

  1. Global aspects of Finsler geometry (T. Aikou and L. Kozma)
  2. Morse theory and nonlinear differential equations (T. Bartsch, A. Szulkin and M. Willem)
  3. Index theory (D. Bleecker)
  4. Partial differential equations on closed and open manifolds (J. Eichhorn)
  5. Spectral geometry (P. Gilkey)
  6. Lagrangian formalism on Grassmann manifolds (D.R. Grigore)
  7. Sobolev spaces on manifolds (E. Hebey and F. Robert)
  8. Harmonic maps (F. Hélein and J.C. Wood)
  9. Topology of differentiable mappings (K. Houston)
  10. Group actions and Hilbert's fifth problem (S. Illman)
  11. Exterior differential systems (N. Kamran)
  12. Weil bundles as generalized jet spaces (I. Kolár)
  13. Distributions, vector distributions, and immersions of manifolds in Euclidean spaces (J. Korbas)
  14. Geometry of differential equations (B. Kruglikov and V. Lychagin)
  15. Global variational theory in fibred spaces (D. Krupka)
  16. Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations (O. Krupková and G.E. Prince)
  17. Elements of noncommutative geometry (G. Landi)
  18. De Rham cohomology (M.A. Malakhaltsev)
  19. Topology of manifolds with corners (J. Margalef-Roig and E. Outerelo Domínguez)
  20. Jet manifolds and natural bundles (D.J. Saunders)
  21. Some aspects of differential theories (J. Szilasi and R.L. Lovas)
  22. Variational sequences (R. Vitolo)
  23. The Oka-Grauert-Gromov principle for holomorphic bundles (P-M. Wong) A. Abstracts


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© Elsevier Science 2008
Elsevier Science
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About the Editor

Demeter Krupka

Affiliations and Expertise

Palacky University, Department of Algebra and Geometry, Olomouc, Czech Republic

David Saunders

Affiliations and Expertise

Visiting professor, Palacky University, Olomouc, Czech Republic