Scenery flow, conical densities, and rectifiability

We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theor...

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Bibliographic Details
Published in:arXiv.org 2017-01
Main Author: Käenmäki, Antti
Format: Article
Language:English
Subjects:
Conical flow
Euclidean geometry
Online Access:Get full text
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Summary:We present an application of the recently developed ergodic theoretic machinery on scenery flows to a classical geometric measure theoretic problem in Euclidean spaces. We also review the enhancements to the theory required in our work. Our main result is a sharp version of the conical density theorem, which we reduce to a question on rectifiability.
ISSN:2331-8422
DOI:10.48550/arxiv.1701.08615