Geometric Aspects of Partial Differential Equations
About this Title
Bernhelm Booss-Bavnbek and Krzysztof Wojciechowski, Editors
This collection of papers by leading researchers gives a broad picture of current research directions in geometric aspects of partial differential equations. Based on lectures presented at a Minisymposium on Spectral Invariants - Heat Equation Approach, held in September 1998 at Roskilde University in Denmark, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field.
Presented here are new index theorems as well as new calculations of the eta-invariant, of the spectral flow, of the Maslov index, of Seiberg-Witten monopoles, heat kernels, determinants, non-commutative residues, and of the Ray-Singer torsion. New types of boundary value problems for operators of Dirac type and generalizations to manifolds with cuspidal ends, to non-compact and to infinite-dimensional manifolds are also discussed. Throughout the book, the use of advanced analysis methods for gaining geometric insight emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on geometric aspects of partial differential equations and spectral invariants.
Graduate students and research mathematicians interested in partial differential equations and global analysis.
Table of Contents
- Christian Bär and David Bleecker – The Dirac operator and the scalar curvature of continuously deformed algebraic varieties [MR 1714476]
- Bogdan Bojarski – The geometry of the Riemann-Hilbert problem [MR 1714477]
- Tosiaki Kori – Chiral anomaly and Grassmannian boundary conditions [MR 1714478]
- Grigori Rozenblum – The index of cone Mellin operators [MR 1714479]
- B. Booss-Bavnbek and K. Furutani – Symplectic functional analysis and spectral invariants [MR 1714480]
- Liviu I. Nicolaescu – Eta invariants, spectral flows and finite energy Seiberg-Witten monopoles [MR 1714481]
- Stuart Dowker, Peter Gilkey and Klaus Kirsten – Heat asymptotics with spectral boundary conditions [MR 1714482]
- Peter Gilkey – Heat content asymptotics [MR 1714483]
- Werner Müller and Katrin Wendland – Extremal Kähler metrics and Ray-Singer analytic torsion [MR 1714484]
- Elmar Schrohe – Noncommutative residues, Dixmier’s trace, and heat trace expansions on manifolds with boundary [MR 1714485]
- Akira Asada – Spectral invariants and geometry of mapping spaces [MR 1714486]
- Jochen Brüning and Matthias Lesch – Spectral theory of boundary value problems for Dirac type operators [MR 1714487]
- Bert-Wolfgang Schulze and Nikolai Tarkhanov – Ellipticity and parametrices on manifolds with cuspidal edges [MR 1714488]
- Mikhail Shubin – Classical and quantum completeness for the Schrödinger operators on non-compact manifolds [MR 1714489]