Jérôme Vétois: McGill University

Speaker: Jérôme Vétois (McGill University)
Time: November 24, Thursday, 4 pm (Indian Standard Time)

Title: Sign-changing blowing-up solutions to the Yamabe equation on a
closed Riemannian manifold

Abstract: In this talk, I will discuss the question of existence of
families of sign-changing solutions to the Yamabe equation, which blow up
in the sense that their maximum values tend to infinity. It is known that
in the case of positive solutions, there does not exist any blowing-up
families of solutions to this problem in dimensions less than 25, except
in the case of manifolds conformally equivalent to the round sphere
(Khuri, Marques and Schoen, 2009). I will present a construction showing
the existence of a non-round metric on spherical space forms of dimensions
greater than 10 for which there exist families of sign-changing blowing-up
solutions to this problem. Moreover, the solutions we construct have the
lowest possible limit energy level. As a counterpart, we will see that
such solutions do not exist at this energy level in dimensions less than
10. This is a joint work with Bruno Premoselli (Université Libre de

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Thu, November 24, 2022
Start Time
4:00pm IST
Created by
Wed, November 23, 2022 11:28am IST