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Volume 9, Issue 4, Article 94 |
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A Non Local Quantitative Characterization of ellipses Leading to a Solvable Differential Relation
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Authors: |
M. Amar, L.R. Berrone, R. Gianni, |
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Keywords:
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Convex sets, asymptotic expansion, ordinary differential equations. |
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Date Received:
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14/02/08 |
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Date Accepted:
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03/07/08 |
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Subject Codes: |
52A10, 41A58, 34A05.
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Editors: |
Catherine Bandle, |
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Abstract: |
In this paper we prove that there are no domains  , other than the ellipses, such that the Lebesgue measure of the intersection of  and its homothetic image  translated to a boundary point  is independent of  , provided that is "centered" at a certain interior point  (the center of homothety).
Similar problems arise in various fields of mathematics, including, for example, the study of stationary isothermal surfaces and rearrangements.
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