## 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

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**Lucio R. Berrone**

CONICET

Departmento de Matematica

Facultad de Ciencias Exactas, Ing. y Agrim.

Universidad Nacional de Rosario

Av. Pellegrine 250, 2000 Rosario

Argentina

e-mail: berrone@fceia.unr.edu.ar