Systolic Geometry And Topology Mikhail G Katz by Mikhail G. Katz 9780821841778, 0821841777 instant download after payment.

This text is based upon a recent course at Bar Ilan University, as well as
upon numerous collaborative efforts (see the Acknowledgments Chapter following
this Preface). After dealing with classical geometric preliminaries, including the
theorema egregium of Gauss, we present new geometric inequalities of systolic type
on Riemann surfaces, as well as their higher dimensional generalisations. Thus, the
text can be viewed as an expanded version of a part of the survey by C. Croke and
the present author [СгКОЗ], which itself dealt with a small part of the material
in M. Gromov’s seminal text Filling Riemannian manifolds [Gro83]. Most of the
results presented here have been obtained over the past four years, a reflection
of the rapid progress in the field since the publication of the monograph [Gro99]
seven years ago. M. Berger’s recent monograph [Berg03] provides a fascinating
historical perspective unburdened by proofs, cf Section 2.1.