Seminar| Institute of Mathematical Sciences
Time：Friday, Apirl 14th, 2023, 15:00-16:00
Location：RS408, IMS
Speaker: 乐鹏宇 (Pengyu Le), 北京雁栖湖应用数学研究院(Yanqi Lake BIMSA)
Abstract: We investigate several conformal invariant functional inequalities on the sphere by interpreting them as inequalities for spacelike sections of the Minkowski lightcone, where the conformal invariance is equivalent to the Lorentz invariance. With this interpretation, we introduce a method combining the symmetrisation and the Lorentz transformation to give a unified proof for a class of conformal invariant functional inequalities, including the reverse Sobolev inequality on the circle, the Moser-Trudinger-Onofri inequality, the sharp Sobolev inequality on the sphere, the Hardy-Littlewood-Sobolev inequality.