, Volume 7, Issue 9, pp 8–18 | Cite as

The Isoperimetric inequality

  • S Kesavan
General Article


A new proof (due to X Cabre) of the classical isoperimetric theorem, based on Alexandrov’s idea of moving planes, will be presented. Compared to the usual proofs, which use geometric measure theory, this proof will be based on elementary ideas from calculus and partial differential equations (Laplace equation).


Isoperimetric inequality moving planes Neumann problem lower contact set elliptic equations 


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Suggested Reading

  1. [1]
    R Courant and H Robbins,What is Mathematics?, Second Edition (revised by Ian Stewart), Oxford University Press, 1996.Google Scholar
  2. [2]
    A Sitaram, The isoperime-tric problem,Resonance, Vol. 2, No. 9, pp. 65–68, 1997.Google Scholar

Copyright information

© Indian Academy of Sciences 2002

Authors and Affiliations

  • S Kesavan
    • 1
  1. 1.The Institute of Mathematical SciencesChennaiIndia

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