Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives - Brossura

Chavel, Isaac

Brossura

ISBN 10: 1107402271 ISBN 13: 9781107402270

Casa editrice: Cambridge University Press, 2011

Riassunto

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 qualitative features of the inequality which 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.

Su questo libro

Recensione:

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

Descrizione del libro:

This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject. It discusses inequalities in Euclidean and Riemannian geometry, methods of classical differential geometry and elementary modern geometric measure theory, discretization of smooth spaces, and the influence of isoperimetric inequalities on heat diffusion on Riemannian manifolds.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 2011
• ISBN 10: 1107402271
• ISBN 13: 9781107402270
• Rilegatura: Copertina flessibile
• Numero di pagine: 282