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Proportionality Principle for the Lipschitz simplicial volume

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Abstract

We prove the Proportionality Principle for the Lipschitz simplicial volume without any restriction on curvature, thus generalizing the main result in Löh and Sauer (J Topol 2(1):193–225, 2009) and the classical Proportionality Principle by Gromov. The cone procedure employed by Löh and Sauer, which is based on the uniqueness of geodesics in Hadamard manifolds, is replaced here by a local construction that exploits the local convexity of general Riemannian manifolds.

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Acknowledgments

This work is part of a Ph. D. Project that I am developing under the supervision of Roberto Frigerio. I would like to thank him for many precious conversations about the subject. I also thank Alberto Abbondandolo and Pietro Majer for helpful comments on Proposition 3.8. Finally, the author is grateful to Clara Löh and Roman Sauer for useful comments on a preliminary version of the paper.

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  1. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127, Pisa, Italy

    Federico Franceschini

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  1. Federico Franceschini
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Correspondence to Federico Franceschini.

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Franceschini, F. Proportionality Principle for the Lipschitz simplicial volume. Geom Dedicata 182, 287–306 (2016). https://doi.org/10.1007/s10711-016-0139-3

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  • DOI: https://doi.org/10.1007/s10711-016-0139-3

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