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Influence of the scalar curvature and the mass on blowing-up solutions to low-dimensional conformally invariant equations.

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we will consider the question of existence of positive blowing-up solutions to a class of conformally invariant elliptic equations of second order on a closed Riemannian manifold. A result of Olivier Druet provides necessary conditions for the existence of blowing-up solutions whose energy is a priori bounded. Essentially, these conditions say that for such solutions to exist, the potential function in the limit equation must coincide, up to a constant factor, at least at one point, with the scalar curvature of the manifold and moreover, in low dimensions, the weak limit of the solutions must be identically zero. I will present new existence results showing the optimality of these conditions. I will discuss in particular the case of low dimensions and the important role of the mass of the Green's function in this case. This is a joint work with Fr\'ed\'eric Robert (Universit\'e de Lorraine).

Mathematics; Partial differential equations; Differential geometry

video/mp4

Author affiliation: McGill University

2019-11-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/72199

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/