Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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.

 

Relations between geometric convexity, doubling measures and property $\Gamma$
HTML articles powered by AMS MathViewer

by Luis A. Caffarelli and Michael G. Crandall PDF
Proc. Amer. Math. Soc. 142 (2014), 2395-2406 Request permission

Abstract:

In this article it is shown that the three conditions on the norm $\left \|\cdot \right \|$ of a Banach space called “geometric convexity”, “balanced” and “doubling” in an earlier work by the authors related to eikonal equations are in fact all equivalent. Moreover, each of them is equivalent to a condition called “Property $\Gamma$” by Ganichev and Kalton. A fifth condition, that the second derivative of the function $t\mapsto \left \|x+ty\right \|$ is a doubling measure on $[-2,2]$ for suitable $x, y\in X,$ is also equivalent to the various other properties, and this formulation occupies a central place in the analysis.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46B20
  • Retrieve articles in all journals with MSC (2010): 46B20
Additional Information
  • Luis A. Caffarelli
  • Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
  • MR Author ID: 44175
  • Email: caffarel@math.utexas.eduu
  • Michael G. Crandall
  • Affiliation: Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106
  • Email: crandall@math.ucsb.edu
  • Received by editor(s): September 9, 2011
  • Received by editor(s) in revised form: June 25, 2012, and July 11, 2012
  • Published electronically: March 21, 2014
  • Additional Notes: The first author was supported in part by NSF Grant DMS-1160802.
  • Communicated by: Thomas Schlumprecht
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2395-2406
  • MSC (2010): Primary 46B20
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11940-X
  • MathSciNet review: 3195762