Metric Structures for Riemannian and Non-Riemannian Spaces

Metric Structures for Riemannian and Non-Riemannian Spaces

Author	Mikhail Gromov
Original title	Structures métriques pour les variétés riemanniennes
Translator	Sean Michael Bates
Country	United States
Language	English
Subject	Mathematics
Genre	Non-fiction
Publisher	Birkhäuser Boston
Publication date	1999
Media type	Print
Pages	xx+585 pp
ISBN	0-8176-3898-9

Metric Structures for Riemannian and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title Structures métriques pour les variétés riemanniennes, by CEDIC (Paris).

History

The 1981 edition was edited by Jacques Lafontaine and Pierre Pansu. The English version, considerably expanded, was published in 1999 by Birkhäuser Verlag, with appendices by Pierre Pansu, Stephen Semmes, and Mikhail Katz. The book was well received^[1]^[2] and has been reprinted several times.

References

↑ Review by Igor Belegradek (MathSciNet)
↑ Review by Mircea Craioveanu (Zentralblatt Math)

Systolic geometry

1-systoles of surfaces	Loewner's torus inequality Pu's inequality Filling area conjecture Bolza surface Systoles of surfaces Eisenstein integers

1-systoles of manifolds	Gromov's systolic inequality for essential manifolds Essential manifold Filling radius Hermite constant

Higher systoles	Gromov's inequality for complex projective space Systolic freedom Systolic category

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