Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Quasiconformal mappings and sets of finite perimeter
HTML articles powered by AMS MathViewer

by James C. Kelly PDF
Trans. Amer. Math. Soc. 180 (1973), 367-387 Request permission

Abstract:

Let $D$ be a domain in ${R^n},n \geqslant 2,f$ a quasiconformal mapping on $D$. We give a definition of bounding surface of codimension one lying in $D$, and show that, given a system $\Sigma$ of such surfaces, the image of the restriction of $f$ to “almost every” surface is again a surface. Moreover, on these surfaces, $f$ takes ${H^{n - 1}}$ (Hausdorff $(n - 1)$-dimensional) null sets to ${H^{n - 1}}$ null sets. “Almost every” surface is given a precise meaning via the concept of the module of a system of measures, a generalization of the concept of extremal length.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A60, 28A75
  • Retrieve articles in all journals with MSC: 30A60, 28A75
Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 180 (1973), 367-387
  • MSC: Primary 30A60; Secondary 28A75
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0357783-7
  • MathSciNet review: 0357783