Spectral Theory and Geometry

doi:10.1017/CBO9780511566165

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.

‘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 Source: Bulletin of the London Mathematical Society

‘For graduate students and experts alike, this book will be a highly useful resource.’

Source: L’Enseignement Mathématique

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Spectral Theory and Geometry

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

1 - Preface
pp vii-vii

2 - List of lecture courses
pp viii-viii

3 - List of participants
pp ix-xii

4 - Basic Riemannian geometry
pp 1-29

5 - The Laplacian on Riemannian manifolds
pp 30-75

6 - Computational Spectral Theory
pp 76-94

7 - Isoperimetric and universal inequalities for eigenvalues
pp 95-139

8 - Estimates of heat kernels on Riemannian manifolds
pp 140-225

9 - Spectral theory of the Schrödinger operators on noncompact manifolds: qualitative results
pp 226-283

10 - Lectures on wave invariants
pp 284-332

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Spectral Theory and Geometry

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