A note on the isoperimetric inequality

Author:
Jani Onninen

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3821-3825

MSC (2000):
Primary 26D10

Published electronically:
June 18, 2003

MathSciNet review:
1999929

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the sharp integral form on the isoperimetric inequality holds for those orientation-preserving mappings whose Jacobians obey the rule of integration by parts.

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Additional Information

**Jani Onninen**

Affiliation:
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland

Address at time of publication:
Department of Mathematics, University of Michigan, 525 E. University Ave., Ann Arbor, MI 48109-1109, USA

Email:
jaonnine@maths.jyu.fi, jonninen@umich.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-06998-3

Received by editor(s):
April 18, 2002

Received by editor(s) in revised form:
July 23, 2002

Published electronically:
June 18, 2003

Additional Notes:
The author was supported in part by the Academy of Finland, project 39788, and by the foundations Magnus Ehrnroothin Säätiö and Vilho, Yrjö ja Kalle Väisälän Rahasto. This research was done when the author was visiting the University of Michigan. He thanks the Department of Mathematics for their hospitality

Communicated by:
Juha M. Heinonen

Article copyright:
© Copyright 2003
American Mathematical Society