Abstract
We study three classes of Lipschitz mappings of the plane: Lipschitz quotient mappings, ball non-collapsing mappings and locally ball non-collapsing mappings. For each class, we estimate the maximum cardinality of point preimage in terms of the ratio of two characteristic constants of the mapping. For Lipschitz quotients and for Lipschitz locally BNC mappings, we provide a complete scale of such estimates, while for the intermediate class of BNC mappings the answer is not complete yet.
Supported by the Israel Science Foundation.
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© 2003 Springer-Verlag Berlin/Heidelberg
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Maleva, O. (2003). Point Preimages under Ball Non-Collapsing Mappings. In: Milman, V.D., Schechtman, G. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1807. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36428-3_13
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DOI: https://doi.org/10.1007/978-3-540-36428-3_13
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00485-1
Online ISBN: 978-3-540-36428-3
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