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A Quantitative Stability Theorem for Convolution on the Heisenberg Group

PDE and Applied Math Seminar

Speaker: Kevin O'Neill, UC Davis
Location: ZOOM
Start time: Fri, May 8 2020, 3:00PM

Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.