This volume brings together lectures from an instructional meeting on spectral theory and geometry held under the auspices of the International Centre for Mathematical Sciences in Edinburgh. The contributions here come from world experts and many are much expanded versions of the lectures they gave. Together they survey the core material and go beyond to reach deeper results. For graduate students and experts alike, this book will be a highly useful resource.
1. Basic Riemannian geometry F. E. Burstall; 2. The Laplacian on Riemannian manifolds I. Chavel; 3. Computational spectral theory E. B. Davies; 4. Isoperimetric and universal inequalities for eigenvalues M. Ashbaugh; 5. Estimates of heat kernels on Riemannian manifolds A. Grigoryan; 6. Spectral theory of the Schroedinger operators on non-compact manifolds: qualitative results M. Shubin; 7. Lectures on wave invariants S. Zelditch.
Reviews for Spectral Theory and Geometry
'The book provides an excellent overview of the relation between the spectral theory of partial differential operators and the geometry of the underlying manifolds.' Dmitri Vassiliev, Bulletin of the London Mathematical Society 'For graduate students and experts alike, this book will be a highly useful resource.' L'Enseignement Mathematique