Improved MoserTrudingerOnofri inequality under constraints
Improved MoserTrudingerOnofri inequality under constraints

Fengbo Hang, Courant Institute, New York University
Fine Hall 314
We will discuss a sequence of MoserTrudinger inequalities on the 2sphere generalizing Aubin's inequality for functions with vanishing first order moments of the area elements to higher order cases. An interesting phenomenon is the appearance of minimal number of nodes for numerical integration on the 2sphere (which is still not known). Our approach also gives a new explanation and proof of the sequence of LebedevMilin type inequalities on the unit circle, which previously were derived from Szego limit theorem (as observed by Widom). These inequalities are partly motivated from the study of isospectral problem on surfaces by OsgoodPhillipsSarnak in late 80’s.