arXiv math/04050192004-05-02math.DGmath.ATmath.GTmath.MG

Generalized degree and optimal Loewner-type inequalities

Sergei V. Ivanov, Mikhail G. Katz

备注：: 13 pages
发表信息：: Published in Israel J. Math. 141 (2004), 221-233

英文摘要：

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.

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