Point Preimages under Ball Non-Collapsing Mappings
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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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