Generalized degree and optimal Loewner-type inequalities
Differential Geometry
2007-05-23 v1 Algebraic Topology
Geometric Topology
Metric Geometry
Abstract
We generalize optimal inequalities of C. Loewner and M. Gromov, by proving lower bounds for the total volume in terms of the homotopy systole and the stable systole. Our main tool is the construction of an area-decreasing map to the Jacobi torus, streamlining and generalizing the construction of the first author in collaboration with D. Burago. It turns out that one can successfully combine this construction with the coarea formula, to yield new optimal inequalities.
Cite
@article{arxiv.math/0405019,
title = {Generalized degree and optimal Loewner-type inequalities},
author = {Sergei V. Ivanov and Mikhail G. Katz},
journal= {arXiv preprint arXiv:math/0405019},
year = {2007}
}
Comments
13 pages