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Title: Porosity and differentiability
Author: Speight, Gareth
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2013
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We investigate porous sets and differentiability of Lipschitz functions. A set P is upper (lower) porous if each point of P sees, on arbitrarily small scales (all sufficiently small scales), nearby holes in P of radius proportional to their distance away. The set P is called directionally upper/lower porous if, for each point of P, the corresponding holes can be chosen with centres on a fixed line. After an overview of porosity and differentiability, we begin by highlighting a difference between upper porosity and lower porosity. Upper porous sets in Rn are necessarily directionally upper porous. We show there exists a lower porous set in R2 which is not even a countable union of directionally lower porous sets. Next we investigate
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics