Isoperimetric Inequalities

Differential Geometric and Analytic Perspectives

By:

Isaac Chavel

Format:

Hardback

Series:

Cambridge Tracts in Mathematics

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Description

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, 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!

Release date NZ

July 23rd, 2001

Author

Isaac Chavel

Audience

Professional & Vocational

Pages

282

Series

Cambridge Tracts in Mathematics

Dimensions

152x229x19

ISBN-13

9780521802673

Product ID

2012283

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