Nonexistence of extremals for the second conformal eigenvalue in low dimensions

Abstract: In this talk, we will consider the second conformal eigenvalue on a closed Riemannian manifold of positive Yamabe type and dimension greater than or equal to 3. The second conformal eigenvalue is defined as the infimum of the second eigenvalue of the conformal Laplacian in a conformal class of metrics with renormalized volume. We will discuss a recent result showing that this infimum is not attained for metrics close to the round metric on the sphere in dimensions 3 to 10, which contrasts sharply with the situation in dimensions greater than or equal to 11, where Ammann and Humbert obtained the existence of minimizers on any closed nonlocally conformally flat manifold. This is a joint work with Bruno Premoselli (Université Libre de Bruxelles).

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic

CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

[[Please provide your first and last name so that the speaker can identify you. Kindly submit your questions or comments using the chat box, not via audio.]]

The livestream is on Zoom at uqam.zoom.us/j/88383789249 It is recommended to subscribe to the CIRGET newsletter. Please send an email to haedrich.alexandra@uqam.ca , providing your name and affiliation.

Some talks can be seen at www.youtube.com/channel/UCLkFm-uEvXSf9y-iQtWOLWA