Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-18T05:49:27.186Z Has data issue: false hasContentIssue false
  • English
  • Français

An elementary proof of the Ambartzumian–Pleijel identity

Published online by Cambridge University Press:  24 October 2008

A. J. Cabo
A. J. Cabo
Affiliation:
CWI, P.O. Box 4079, 1009 AB Amsterdam, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Extract

In [5], Pleijel proved an identity relating the area A of a convex plane domain and the length L of its boundary (of class C1). In particular, it contains the isoperimetric inequality L2 –4πA ≥ 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 3 , November 1992 , pp. 535 - 538
Copyright
Copyright © Cambridge Philosophical Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ambartzumian, R. V.. Convex polygons and random tessellations. In Stochastic Geometry: A Tribute to the memory of Rollo Davidson (Wiley. 1974), pp. 176–191.Google Scholar
[2]Ambartzumian, R. V.. Combinatorial Integral Geometry (Wiley, 1982).Google Scholar
[3]Cabo, A. J.. Chordlength distributions and characterization problems for convex plane polygons. Master's thesis, University of Amsterdam (1989).Google Scholar
[4]Guillemin, V. and Pollack, A.. Differential Topology (Prentice-Hall, 1974).Google Scholar
[5]Pleijel, A.. Zwei kurze Beweise der isoperimetrischen Ungleichung. Arch. Math. (Basel) 1 (1956), 317–319.Google Scholar
[6]Pohl, W. F.. The probability of linking of random closed curves. In Geometry Symposium Utrecht, Lecture Notes in Math. vol. 894 (Springer-Verlag, 1980), pp. 113–126.CrossRefGoogle Scholar