Highly Influenced

9 Excerpts

@inproceedings{Amar2008ANL, title={A NON LOCAL QUANTITATIVE CHARACTERIZATION OF ELLIPSES LEADING TO A SOLVABLE DIFFERENTIAL RELATION}, author={Makhlouf Amar and Lucio R. Berrone and Roberto Gianni}, year={2008} }

- Published 2008

In this paper we prove that there are no domains E ⊂ R, other than the ellipses, such that the Lebesgue measure of the intersection of E and its homothetic image εE translated to a boundary point q ∈ ∂E is independent of q, provided thatE is "centered" at a certain interior pointO ∈ E (the center of homothety). Similar problems arise in various fields of mathematics, including, for example, the study of stationary isothermal surfaces and rearrangements.