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Cambridge Studies in Advanced Mathematics: Series Number 98
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Table of Contents

1. Riemannian manifolds; 2. Riemannian curvature; 3. Riemannian volume; 4. Riemannian coverings; 5. Surfaces; 6. Isoperimetric inequalities (constant curvature); 7. The kinetic density; 8. Isoperimetric inequalities (variable curvature); 9. Comparison and finiteness theorems.

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This corrected and clarified second edition, first published in 2006, includes a new chapter on the Riemannian geometry of surfaces.

About the Author

Isaac Chavel is Professor of Mathematics at The City College of the City University of New York. He received his Ph.D. in Mathematics from Yeshiva University under the direction of Professor Harry E. Rauch. He has published in international journals in the areas of differential geometry and partial differential equations, especially the Laplace and heat operators on Riemannian manifolds. His other books include Eigenvalues in Riemannian Geometry, Academic Press, 1984, and Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives, Cambridge U. Press, 2001. He has been teaching at The City College of the City University of New York since 1970, and has been a member of the doctoral program of the City University of New York since 1976. He is a member of the American Mathematical Society.

Reviews

'... I think that it is the best reference on Riemannian geometry available, especially for someone interested in isoperimetric problems. ... an insightful modern perspective on topics of current research interest.' SIAM Review

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