Yi Wang, Stanford University
"Isoperimetric inequality and Q-curvature"
A well-known question in differential geometry is to prove the isoperimetric inequality under intrinsic curvature conditions. In dimension 2, the isoperimetric inequality is controlled by the integral of the positive part of the Gaussian curvature. In my recent work, I prove that on simply connected conformally flat manifolds of higher dimensions, the role of the Gaussian curvature can be replaced by the Branson's Q-curvature. The isoperimetric inequality is valid if the integral of the Q-curvature is below a sharp threshold. Moreover, the isoperimetric constant depends only on the integrals of the Q-curvature. The proof relies on the theory of $A_p$ weights in harmonic analysis.
Refreshments will be served in MC 5046 at 3:30 pm. Everyone is welcome to attend.