14 jan 2021 -- 17:00
Differential Geometry Seminar Torino (online)
Abstract.
The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure $\mu$, the Alexandrov problem consists in proving the existence and uniqueness of a convex body whose curvature measure is $\mu$.
In the Euclidean space, this problem was first solved by Alexandrov, and it was observed later that it is equivalent to an optimal transport problem on the sphere. In this talk I will consider Alexandrov problem for convex bodies of the hyperbolic space. After defining the curvature measure, I will explain what are its main properties. If time permits, I will explain how the optimal transport approach of Alexandrov problem leads to a non-linear Kantorovich problem on the sphere, and how to solve it.
Joint work with Jérôme Bertrand.
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The talks are presented using the platform Cisco Webex Meetings. The Webex link will be sent one day before the talk to all registered participants. To register, please send an e-mail to dgseminar.torino@gmail.com