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Synopsis
This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
Booknews
As part of a series whose volumes pursue a narrow path in a broad subject, this introductory tract follows two venues of the isoperimetric inequality which span the evolution from the Euclidian space of classical differential geometry to the inequalities of modern measure theory. The treatment of Riemann manifolds is guided by the dichotomy between their local Euclidian character and global geometric properties, and covers discretization techniques and application to large time heat diffusion problems. Chapters include proofs. Chavel (mathematics, City U. of New York) is the author of and . Annotation c. Book News, Inc., Portland, OR (booknews.com)