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Generalized degree and optimal loewner-type inequalities

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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.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Fontanka 27, RU-191011, St. Petersburg, Russia

    Sergei V. Ivanov

  2. Department of Mathematics and Statistics, Bar Ilan University, 52900, Ramat Gan, Israel

    Mikhail G. Katz

Authors
  1. Sergei V. Ivanov
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  2. Mikhail G. Katz
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Corresponding author

Correspondence to Sergei V. Ivanov.

Additional information

Supported by grants CRDF RM1-2381-ST-02, RFBR 02-01-00090 and NS-1914.2003.1.

Supported by the Israel Science Foundation (grants no. 620/00-10.0 and 84/03).

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Ivanov, S.V., Katz, M.G. Generalized degree and optimal loewner-type inequalities. Isr. J. Math. 141, 221–233 (2004). https://doi.org/10.1007/BF02772220

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  • DOI: https://doi.org/10.1007/BF02772220

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