Spectral Theory and Geometry

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.

Preface

vii

List of lecture courses

viii

List of participants

ix

Basic Riemannian geometry

1

(29)

F E Burstall

The Laplacian on Riemannian manifolds

30

(46)

I Chavel

Computational spectral theory

76

(19)

E B Davies

Isoperimetric and universal inequalities for eigenvalues

95

(45)

M Ashbaugh

Estimates of heat kernels on Riemannian manifolds

140

(86)

M Grigor'yan

Spectral theory of the Schrodinger operators on noncompact manifolds: qualitative results

226

(58)

M Shubin

Lectures on wave invariants

284

S Zelditch

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Spectral Theory and Geometry

Summary

Table of Contents

Supplemental Materials