University of Connecticut

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Analysis and Probability Seminar
Improved Moser-Trudinger-Onofri Inequality on the Sphere
Fengbo Hang (NYU)

Friday, March 27, 2020
1:30pm – 2:30pm

Storrs Campus
MONT 313

Abstract: We will discuss a sequence of Moser-Trudinger-Onofri inequalities on the n-sphere generalizing Aubin's inequality for functions with vanishing first order moments of the area element to higher order cases. A crucial ingredient is refinements of concentration compactness principle in critial dimensions. It is interesting that minimal number of nodes for numerical integration on the n-sphere appear in these new inequalities. On the unit circle, these inequalities are related to the log determinant of Laplacian under Dirichlet boundary condition on surface with boundary by Osgood-Phillips-Sarnack in late 80's, and they were previously derived from Szego limit theorem (as observed by Widom). On the 2-sphere, they are closely related to isospectral problem and Gauss curvature equations.


Analysis and Probability Seminar (primary), UConn Master Calendar

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