We analyse three different stability problems for functional inequalities. We investigate Gagliardo—Nirenberg inequalities on the sphere, and Beckner’s inequalities in the Gaussian space, as a rigorous infinite-dimensional limit of those. Finally, as the critical endpoint of Beckner’s inequalities, we consider the Gaussian LSI. Stability results are provided, in a constructive fashion, via a new flow-based technique, combined with spectral analysis, and precise Taylor developments. The presentation is based on a series of paper by Jean Dolbeault, Nikita Simonov, and the speaker.
Jérémy Heleine, David Lafontaine
