Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 99-123

CURVATURE INTEGRAL AND LIPSCHITZ PARAMETRIZATION IN 1-REGULAR METRIC SPACES

Immo Hahlomaa

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 Jyväskylä, Finland; imhahlom 'at' maths.jyu.fi

Abstract. We show that for a bounded 1-regular metric measure space (E,\mu) the finiteness of the Menger curvature integral

\int_E\int_E\int_E c(z₁,z₂,z₃)² d\mu z₁ d\mu z₂ d\mu z₃

guarantees that E is a Lipschitz image of a subset of a bounded subinterval of R.

2000 Mathematics Subject Classification: Primary 28A75; Secondary 51F99.

Key words: Menger curvature, Lipschitz parametrization.

Reference to this article: I. Hahlomaa: Curvature integral and Lipschitz parametrization in 1-regular metric spaces. Ann. Acad. Sci. Fenn. Math. 32 (2007), 99-123.

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