Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics, Series Number 145) - Hardcover

Chavel, Isaac

Hardcover

ISBN 10: 0521802679 ISBN 13: 9780521802673

Publisher: Cambridge University Press, 2001

Synopsis

This introduction treats the classical isoperimetric inequality in Euclidean space and contrasting rough inequalities in noncompact Riemannian manifolds. In Euclidean space the emphasis is on a most general form of the inequality sufficiently precise to characterize the case of equality, and in Riemannian manifolds the emphasis is on those qualitiative features of the inequality that provide insight into the coarse geometry at infinity of Riemannian manifolds. The treatment in Euclidean space features a number of proofs of the classical inequality in increasing generality, providing in the process a transition from the methods of classical differential geometry to those of modern geometric measure theory; and the treatment in Riemannian manifolds features discretization techniques, and applications to upper bounds of large time heat diffusion in Riemannian manifolds. The result is an introduction to the rich tapestry of ideas and techniques of isoperimetric inequalities, a subject that has its beginnings in classical antiquity and which continues to inspire fresh ideas in geometry and analysis to this very day--and beyond!

About this title

Book Description

Classical isoperimetric inequalities in the plane relate the area of a domain to the length of its boundary, and, in space, the volume to the area of its boundary. This advan ced introduction emphasizes the subject's variety of ideas, techniques, and applications. The author discusses inequalities in Euclidean and Riemannian geometry, methods of classical differential geometry and elementary modern geometric measure, discretization of smooth spaces, and the influence of isoperimetric inequalities on heat diffusion on Riemannian manifolds.Requiring only of a basic course in differential geometry, this book will appeal to graduate students and researchers alike in differential geometry, analysis, and related subjects.

Review

Review of the hardback: 'The presentation of the book is clear and elegant, and gives expression to the beauty of the subject. It is a great pleasure to read this book, which is a profound source text for both classical and modern methods, and which will be equally valuable to graduate students and researchers in analysis and geometry.' Bulletin of the London Mathematical Society

Review of the hardback: 'The book is very useful in two ways. First, it nicely explains the story of the classical isoperimetric inequality, a result with a big disproportion between the ease of formulation and difficulty of the proof. This second part contains deep results obtained by the author.' European Mathematical Society

Review of the hardback: '... very useful ...' EMS Newsletter

Review of the hardback: '[This book] constitues a valuable addition to the modern theory of inequalities.' Bulletin of the Belgian Mathematical Society

Edition details

• Publisher: Cambridge University Press
• Publication date: 2001
• ISBN 10: 0521802679
• ISBN 13: 9780521802673
• Binding: Hardcover
• Language: English
• Edition number: 1
• Number of pages: 282