Unique determination of ellipsoids by their dual volumes

Tuesday, September 22, 2020 - 2:00pm
Vlad Yaskin
(University of Alberta)

Gusakova and Zaporozhets conjectured that ellipsoids in
$\mathbb R^n$ are uniquely determined (up to an isometry) by their
intrinsic volumes. Petrov and Tarasov confirmed this conjecture in
$\mathbb R^3$. In this talk we will present a solution to the dual
problem in all dimensions. We will show that any ellipsoid in $\mathbb
R^n$ centered at the origin is uniquely determined (up to an isometry)
by an $n$-tuple of its dual volumes. To prove this result we reduce it
to a problem of moments. As an application, we give an alternative
proof of the result of Petrov and Tarasov. This is a joint work with
S. Myroshnychenko and K. Tatarko.


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