Use this URL to cite or link to this record in EThOS:
Title: Some questions related to the Analyst's TST and a conjecture of Carleson
Author: Villa, Michele
ISNI:       0000 0004 8510 4780
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2020
Availability of Full Text:
Access from EThOS:
Full text unavailable from EThOS. Please try the link below.
Access from Institution:
This thesis is constituted by two independent parts. In the first part we discuss several problems which relate to the Analyst's Travelling Salesman Theorem of Peter Jones and the theories of uniformly rectifiable sets and quasiminimal sets of David and Semmes. To say more, this first part splits naturally into two chapters, which are nevertheless connected. In a first chapter, we present a joint work with Jonas Azzam which shows that, in some sense, there exists a travelling salesman theorem for each property that characterises uniformly rectifiable sets. In a second chapter, we address the question of what type of geometric object can play the role of a curve in a higher dimensional setting, at least from the point of view of an Analyst's TST. The second part of this thesis is dedicated to presenting a joint work with Benjamin Jaye and Xavier Tolsa which settles a longstanding conjecture of Carleson, known in the field as Carleson ve² conjecture, in a positive sense.
Supervisor: Azzam, Jonas ; Gimperlein, Heiko Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
Keywords: mathematical analysis ; Euclidean space ; uniform rectifiability