Maximal Functions, Incidence Theorems, and Efficient Partitions of Euclidean Space
Posted on:2014-12-16
Degree:Ph.D
Type:Dissertation
University:University of California, Los Angeles
Candidate:Zahl, Joshua Norbert
Full Text:PDF
GTID:1450390008951119
Subject:Mathematics
Abstract/Summary:
We establish several new results in incidence geometry and harmonic analysis. Each of the problems we consider is about objects in Euclidean space, and we make essential use of partitioning theorems that efficiently cut Rd into pieces that have desirable combinatorial properties.