Speaker
Xavier Lamy
(IMT, UPS - Toulouse 3)
Description
A classical theorem of Liouville asserts that if a map from the sphere to itself is conformal, then it must be a Möbius map: a composition of dilations, rotations, inversions and translations (identifying sphere and euclidean space via stereographic projection). There is a long history of studying stability of this rigidity statement: if a map is nearly conformal, must it be close to a Möbius transform? One can also ask what happens if the image of the map is only nearly spherical. I will present sharp stability estimates obtained recently with André Guerra and Kostantinos Zemas.
