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Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives by Isaac Chavel

Isoperimetric Inequalities: Differential Geometric and Analytic Perspectives

by Isaac Chavel
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Book cover type: Paperback
  • ISBN13: 9781107402270
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Publication Date:
  • Pages: 282
  • Original Price: GBP 57.0
  • Language: English
  • Edition: Reissue
  • Item Weight: 418 grams
  • BISAC Subject(s): Geometry / Differential

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!

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