A one-dimensional planar Besicovitch-type set
Iqra Altaf

TL;DR
This paper constructs a non-trivial 1-rectifiable set in the plane that contains rotated copies of a specific set in every direction, advancing the understanding of Besicovitch-type sets in geometric measure theory.
Contribution
It introduces a new example of a 1-rectifiable set with a Besicovitch-type property, expanding the class of known Besicovitch sets in the plane.
Findings
Existence of a 1-rectifiable $ ext{Gamma}$-Besicovitch set in the plane.
Construction of a non-trivial $ ext{Gamma}$-Besicovitch set with specific rectifiability.
Advancement in understanding geometric configurations containing rotated copies in all directions.
Abstract
A -Besicovitch set is a set which contains a rotated copy of in every direction. Our main result is the construction of a non-trivial -rectifiable set in the plane, for which there exists a 1-dimensional -Besicovitch set.
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Taxonomy
TopicsMathematics and Applications
