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

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

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