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On equichordal curves

Published online by Cambridge University Press:  14 November 2011

Waldemar Cieślak
Waldemar Cieślak
Affiliation:
Institute of Mathematics, Maria Curie Skłodowska University, Lublin, Poland
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Synopsis

In this paper we consider equichordal curves in ℝn. We extend the notion of chordal area to all equichordal curves and introduce a notion of *-chordal area. We establish results connected with the length, *-chordal area and extended chordal area. Moreover, we give a Crofton-type integral formula for plane equichordal curves and derive an isoperimetric inequality for *-chordal area. The paper is based on the results of F. J. Craveiro de Carvalho and S. A. Robertson [2].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 105 - 110
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Cieślak, W.. Crofton-type integral formulas for star domain. Geom. Dedicata 28 (1988), 251–258.CrossRefGoogle Scholar
2Craveiro de Carvalho, F. J. and Robertson, S. A.. Equichordal curves. Proc. Roy. Soc. EdinburghSect. A 110 (1988), 85–91.CrossRefGoogle Scholar
3Sternberg, S.. Lectures on differential geometry (Englewood Cliffs, N.J. Prentice Hall, 1964).Google Scholar
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