Generalized degree and optimal Loewner-type inequalities

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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.
13 pages

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Differential Geometry, Algebraic Topology, Geometric Topology, Metric Geometry, 53C23; 57N65;52C07

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http://salesiana.dossiersoluciones.com/handle/123456789/71036

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0405019
 http://arxiv.org/abs/math/0405019
 Published in Israel J. Math. 141 (2004), 221-233

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arXiv