A Non Local Quantitative Characterization of Ellipses Leading to a Solvable Differential Relation
نویسندگان
چکیده
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 εE translated to a boundary point q ∈ ∂E is independent of q, provided that E is ”centered” at a certain interior point O ∈ E (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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