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## Details

Material Type: | Internet resource |
---|---|

Document Type: | Book, Internet Resource |

All Authors / Contributors: |
Mikhail Gersh Katz |

ISBN: | 9780821841778 0821841777 |

OCLC Number: | 77716978 |

Description: | xiv, 222 p. : ill. ; 26 cm. |

Contents: | Historical remarks; The theorema egregium of Gauss; Global geometry of surfaces; Inequalities of Loewner and Pu; Systolic applications of integral geometry; A primer on surfaces; Filling area theorem for hyperelliptic surfaces; Hyperelliptic surfaces are Loewner; An optimal inequality for CAT(0) metrics; Volume entropy and asymptotic upper bounds; Gromov's optimal stable systolic inequality for $mathbb{CP}n$; Systolic inequalities dependent on Massey products; Cup products and stable systoles; Dual-critical lattices and systoles; Generalized degree and Loewner-type inequalities; Higher inequalities of Loewner-Gromov type; Systolic inequalities for $Lp$ norms; Four-manifold systole asymptotics; Period map image density (by Jake Solomon); Open problems; Bibliography; Index |

Series Title: | Mathematical surveys and monographs, no. 137. |

Responsibility: | Mikhail G. Katz ; with an appendix by Jake P. Solomon. |

### Abstract:

Presents the systolic geometry of manifolds and polyhedra, starting with the two classical inequalities. This book features Gromov's inequalities and their generalisations, as well as asymptotic phenomena for systoles of surfaces of large genus, revealing a link both to ergodic theory and to properties of congruence subgroups of arithmetic groups.
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## Similar Items

### Related Subjects:(15)

- Geometry, Algebraic.
- Riemann surfaces.
- Topology.
- Inequalities (Mathematics)
- Géométrie algébrique.
- Riemann, Surfaces de.
- Topologie.
- Inégalités (Mathématiques)
- Topologia.
- Geometria global.
- Geometria diferencial (textos avançados)
- Variedades riemannianas.
- Geometrische Invariantentheorie.
- Riemannsche Fläche.
- Topologische Mannigfaltigkeit.