Menger curvature and regularity of fractals

Authors:
Yong Lin and Pertti Mattila

Journal:
Proc. Amer. Math. Soc. **129** (2001), 1755-1762

MSC (2000):
Primary 28A75

Published electronically:
October 31, 2000

MathSciNet review:
1814107

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Abstract | References | Similar Articles | Additional Information

We show that if is an -regular set in for which the triple integral of the Menger curvature is finite and if , then almost all of can be covered with countably many curves. We give an example to show that this is false for .

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Additional Information

**Yong Lin**

Affiliation:
Department of Mathematics, Renmin University of China, Information School, Beijing, 100872, China

Email:
liny9@263.net

**Pertti Mattila**

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

Email:
pmattila@math.jyu.fi

DOI:
https://doi.org/10.1090/S0002-9939-00-05814-7

Received by editor(s):
September 27, 1999

Published electronically:
October 31, 2000

Additional Notes:
The authors gratefully acknowledge the hospitality of CRM at Universitat Autònoma de Barcelona where part of this work was done. The first author also wants to thank the Academy of Finland for financial support.

Communicated by:
Albert Baernstein II

Article copyright:
© Copyright 2000
American Mathematical Society