Mapping n grid points onto a square forces an arbitrarily large Lipschitz constant.

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• Michael Dymond (Innsbruck)
• Wednesday 27 February 2019, 10:00-11:00
• PHYW-SR1 (103).

If you have a question about this talk, please contact Diogo Oliveira E Silva.

We discuss a recent work which proves that the regular nxn square grid of points in the integer lattice ZxZ cannot be recovered from an arbitrary n2-element subset of ZxZ via a mapping with prescribed Lipschitz constant (independent of n). This answers negatively a question of Feige. Our resolution of Feige’s question takes place largely in a continuous setting and is based on some new results for Lipschitz mappings falling into two broad areas of interest, which we study independently. Firstly we discuss Lipschitz regular mappings on Euclidean spaces, with emphasis on their bilipschitz decomposability in a sense comparable to that of the well known result of Jones. Secondly, we build on work of Burago and Kleiner and McMullen on non-realisable densities. We verify the existence, and further prevalence, of strongly non-realisable densities inside spaces of continuous functions. This is joint work with Vojtech Kaluza and Eva Kopecká.

This talk is part of the Analysis seminar series.

This talk is included in these lists:

• Analysis seminar
• PHYW-SR1 (103)
• School of Mathematics events

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