Components of level sets of uniform co-Lipschitz functions on the plane
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- by Olga Maleva PDF
- Proc. Amer. Math. Soc. 133 (2005), 841-850 Request permission
Abstract:
Consider a co-Lipschitz uniformly continuous function $f$ defined on the plane. Let $n(f)$ be the maximal number of components of its level set. In the present paper we settle a question of B. Randrianantoanina, concerning the dependence of $n(f)$ on the quantitative characteristics of the mapping. We prove that $n(f)$ is bounded from above by a simple function of the co-Lipschitz and the “weak Lipschitz” constants of $f$, and show that our estimate is sharp. We also prove additional properties of the level sets.References
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Additional Information
- Olga Maleva
- Affiliation: Department of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel
- Address at time of publication: Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
- Email: olga@math.ucl.ac.uk
- Received by editor(s): November 5, 2002
- Received by editor(s) in revised form: November 20, 2003
- Published electronically: September 29, 2004
- Additional Notes: The author was supported by the Israel Science Foundation.
- Communicated by: David Preiss
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 841-850
- MSC (2000): Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-04-07657-9
- MathSciNet review: 2113935