Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.

 

Range of the gradient of a smooth bump function in finite dimensions
HTML articles powered by AMS MathViewer

by Ludovic Rifford PDF
Proc. Amer. Math. Soc. 131 (2003), 3063-3066 Request permission

Abstract:

This paper proves the semi-closedness of the range of the gradient for sufficiently smooth bumps in the Euclidean space.
References
  • J. M. Borwein, M. Fabian, I. Kortezov, and P. D. Loewen, The range of the gradient of a continuously differentiable bump, J. Nonlinear Convex Anal. 2 (2001), no. 1, 1–19. Special issue for Professor Ky Fan. MR 1828155
  • Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
  • T. Gaspari. On the range of the derivative of a real valued function with bounded support. Preprint.
  • Walter Rudin, Principles of mathematical analysis, 2nd ed., McGraw-Hill Book Co., New York, 1964. MR 0166310
  • Michael Spivak, A comprehensive introduction to differential geometry. Vol. I, 2nd ed., Publish or Perish, Inc., Wilmington, Del., 1979. MR 532830
  • X. Wang. Pathological examples of Lipschitz functions. Ph.D. thesis, SFU, 1995.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46G05, 58C25
  • Retrieve articles in all journals with MSC (2000): 46G05, 58C25
Additional Information
  • Ludovic Rifford
  • Affiliation: Institut Girard Desargues, Université Claude Bernard Lyon I, 69622 Villeurbanne, France
  • Email: rifford@igd.univ-lyon1.fr
  • Received by editor(s): April 16, 2002
  • Published electronically: March 11, 2003
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 3063-3066
  • MSC (2000): Primary 46G05, 58C25
  • DOI: https://doi.org/10.1090/S0002-9939-03-07078-3
  • MathSciNet review: 1993214