香蕉视频

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 (Universit茅 Libre de Bruxelles).

Zoom link:

Meeting ID: 831 1853 9851

Passcode: 215516

Room: 4336-4384 Pav. Andr茅-Aisentadt (CRM)