Curve packing and modulus estimates

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http://hdl.handle.net/10138/307142

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Fassler , K & Orponen , T 2018 , ' Curve packing and modulus estimates ' , Transactions of the American Mathematical Society , vol. 370 , no. 7 , pp. 4909-4926 . https://doi.org/10.1090/tran/7175

Title: Curve packing and modulus estimates
Author: Fassler, Katrin; Orponen, Tuomas
Contributor organization: Department of Mathematics and Statistics
Date: 2018-07
Language: eng
Number of pages: 18
Belongs to series: Transactions of the American Mathematical Society
ISSN: 0002-9947
DOI: https://doi.org/10.1090/tran/7175
URI: http://hdl.handle.net/10138/307142
Abstract: A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in R-2 of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family always has area at least c for some small absolute constant c > 0. We strengthen Marstrand's result by showing that for p > 3, the p-modulus of a Moser family of curves is at least c(p) > 0.
Subject: MEASURE ZERO
THIN SET
CIRCLES
111 Mathematics
Peer reviewed: Yes
Usage restriction: openAccess
Self-archived version: acceptedVersion


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