The Convenient Setting of Global Analysis
by Andreas Kriegl, Peter W. Michor
Publisher: American Mathematical Society 1997
ISBN/ASIN: 0821807803
ISBN-13: 9780821807804
Number of pages: 624
Description:
This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. Many applications are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
Download or read it online for free here:
Download link
(4MB, PDF)
Similar books
Natural Operations in Differential Geometryby Ivan Kolar, Peter W. Michor, Jan Slovak - Springer
A comprehensive textbook on all basic structures from the theory of jets. It begins with an introduction to differential geometry. After reduction each problem to a finite order setting, the remaining discussion is based on properties of jet spaces.
(18314 views)
Notes on the Atiyah-Singer Index Theoremby Liviu I. Nicolaescu - University of Notre Dame
This is arguably one of the deepest and most beautiful results in modern geometry, and it is surely a must know for any geometer / topologist. It has to do with elliptic partial differential operators on a compact manifold.
(12943 views)
Geometric Wave Equationsby Stefan Waldmann - arXiv
We discuss the solution theory of geometric wave equations as they arise in Lorentzian geometry: for a normally hyperbolic differential operator the existence and uniqueness properties of Green functions and Green operators is discussed.
(12345 views)
Lectures on Minimal Surface Theoryby Brian White - arXiv
The goal was to give beginning graduate students an introduction to some of the most important basic facts and ideas in minimal surface theory. Prerequisites: the reader should know basic complex analysis and elementary differential geometry.
(10121 views)