A non local quantitative characterization of ellipsis leading to a solvable differential relation

M. AMAR, L. R. BERRONE, R. GIANNI

Journal of Inequalities in Pure and Applied Mathematics

Año: 2008 vol. 9 p. 1 - 14

ABSTRACT. In this paper we prove that there are no domains E. R2, other than the ellipses,such that the Lebesgue measure of the intersection of E and its homothetic image "E translatedto a boundary point q . @E is independent of q, provided that E is "centered" at a certain interiorpoint O 2E (the center of homothety).Similar problems arise in various fields of mathematics, including, for example, the study ofstationary isothermal surfaces and rearrangements. Key words and phrases: Convex sets, asymptotic expansion, ordinary differential equations. 2000 Mathematics Subject Classification. 52A10, 41A58, 34A05.