The Kakeya needle problem and the existence of Besicovitch and Nikodym sets for rectifiable sets
Alan Chang, Marianna Cs\"ornyei
TL;DR
This paper addresses the Kakeya needle problem and constructs Besicovitch and Nikodym sets specifically for rectifiable sets, advancing understanding in geometric measure theory.
Contribution
It provides the first solutions to the Kakeya needle problem and constructs Besicovitch and Nikodym sets tailored for rectifiable sets, a novel development in the field.
Findings
Solved the Kakeya needle problem for rectifiable sets
Constructed Besicovitch sets for rectifiable sets
Constructed Nikodym sets for rectifiable sets
Abstract
We solve the Kakeya needle problem and construct a Besicovitch and a Nikodym set for rectifiable sets.
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