Curve packing and modulus estimates
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 has always 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 cp > 0.
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
American Mathematical Society
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201810034316Use this for linking
Review status
Peer reviewed
ISSN
0002-9947
DOI
https://doi.org/10.1090/tran/7175
Language
English
Published in
Transactions of the American Mathematical Society
Citation
- Fässler, K., & Orponen, T. (2018). Curve packing and modulus estimates. Transactions of the American Mathematical Society, 370(7), 4909-4926. https://doi.org/10.1090/tran/7175
License
Copyright© 2018 American Mathematical Society