ENGLISH

Isoperimetric inequalities: differential geometric and analytic perspectives

By Isaac Chavel

Book information

Publisher
Cambridge University Press
Year
2001
ISBN
0521802679, 9780521802673
Open Library ID
OL18729222M
Language
english
Format
DJVU
Filesize
2 MB (2202499 bytes)
Series
Cambridge tracts in mathematics 145
Pages
141\141
Library
Kolxo3
DPI
300
Scanned
landscape
Time added
2009-07-20 03:45:11

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 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!

Similar books