Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Prescribing the Gauss curvature of hyperbolic convex bodies

Philippe Castillon

created by raffero on 29 Dec 2020
modified on 07 Jan 2021

14 jan 2021 -- 17:00

Differential Geometry Seminar Torino (online)


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.


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

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