Beurling's criterion and extremal metrics for Fuglede modulus
Abstract
We formulate a necessary and sufficient condition for an admissible metric to be extremal for the Fuglede pmodulus of a system of measures. When p=2, this characterization generalizes Beurling's criterion, a sufficient condition for an admissible metric to be extremal for the extremal length of a planar curve family. In addition, we prove that every nonnegative Borel function in R^n with positive and finite pnorm is extremal for the pmodulus of some curve family.
 Publication:

arXiv eprints
 Pub Date:
 July 2012
 DOI:
 10.48550/arXiv.1207.5277
 arXiv:
 arXiv:1207.5277
 Bibcode:
 2012arXiv1207.5277B
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Metric Geometry;
 31B15 (Primary) 28A33;
 49K27 (Secondary)
 EPrint:
 12 pages, 2 figures (version 4: minor improvements, updated numbering and corrected typos, final version)