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5 - Weak Tangents and Microsets

from Part One - Theory

Published online by Cambridge University Press:  13 October 2020

Jonathan M. Fraser
Jonathan M. Fraser
Affiliation:
University of St Andrews, Scotland
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Summary

One of the most effective ways to bound the Assouad dimension of a set from below is to use weak tangents; an approach pioneered by Mackay and Tyson. Weak tangents are tools for capturing the extremal local structure of a set. In this chapter we explore this connection. We prove Mackay and Tyson's estimate, and a stronger result of Furstenberg which characterises the Assouad dimension entirely in terms of the Hausdorffdimension of weak tangents.

Keywords

weak tangentmicroset
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Chapter
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Assouad Dimension and Fractal Geometry , pp. 64 - 78
Publisher: Cambridge University Press
Print publication year: 2020

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