Curve packing and modulus estimates
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
Published inTransactions of the American Mathematical Society
© 2018 American Mathematical Society
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.
PublisherAmerican Mathematical Society
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Hofmann, Steve; Tapiola, Olli (Centre Mersenne; l'Institut Fourier,, 2020)Suppose that E⊂Rn+1 is a uniformly rectifiable set of codimension 1. We show that every harmonic function is ε-approximable in Lp(Ω) for every p∈(1,∞), where Ω:=Rn+1∖E. Together with results of many authors this shows that ...
Lohvansuu, Atte (Finnish Mathematical Society, 2021)We generalize a result of Freedman and He [4, Theorem 2.5], concerning the duality of moduli and capacities in solid tori, to sufficiently regular metric spaces. This is a continuation of the work of the author and Rajala ...
Rajala, Kai; Rasimus, Martti; Romney, Matthew (Springer, 2021)We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces X homeomorphic to R2R2. Given a measure μμ on such a space, we introduce μμ-quasiconformal maps f:X→R2f:X→R2, ...
Rajala, Kai; Romney, Matthew (Suomalainen tiedeakatemia, 2019)
The Missing Member of the Partially O-Alkylated Resorcinarene Family: Synthesis and Conformation of Methyl Tetramethoxy Resorcinarene Tero, Tiia-Riikka; Suhonen, Aku; Salorinne, Kirsi; Campos-Barbosa, Hélène; Nissinen, Maija (American Chemical Society, 2013)An improved Lewis acid catalyzed synthesis method for methyl tetramethoxy resorcinarene is described, which produced the missing lower rim methyl derivative of this partially O-alkylated resorcinarene family. Structural ...