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Point Preimages under Ball Non-Collapsing Mappings

  • Olga MalevaEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1807)

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.

Mathematics Subject Classification (2000):

46-06 46B07 52-06 60-06 

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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