Uniqueness of Ellipsoidal Solutions to a Geometric Problem (Open)

Summary: The problem consists of deciding whether domains $B \subset \mathbb{R}^{n}$ other than ellipsoidal ones exist such that the Lebesgue measure of the intersection of B and its homothetic image $\varepsilon B$ translated to a boundary point x is independent of x, given that B is "centered" at a certain interior point O (the center of homothety).

Classification: Primary, Geometry; Secondary, n-dimensional Euclidean geometry

Lucio R. Berrone
Departmento de Matematica
Facultad de Ciencias Exactas, Ing. y Agrim.
Universidad Nacional de Rosario
Av. Pellegrine 250, 2000 Rosario
e-mail: berrone@fceia.unr.edu.ar

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