Ebook Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics), by Isaac Chavel
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Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics), by Isaac Chavel
Ebook Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives (Cambridge Tracts in Mathematics), by Isaac Chavel
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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!
- Sales Rank: #4160831 in Books
- Brand: Brand: Cambridge University Press
- Published on: 2001-07-23
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .75" w x 5.98" l, 1.15 pounds
- Binding: Hardcover
- 282 pages
- Used Book in Good Condition
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
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