Differential Geometry Seminar

Speaker: 
Ali Hyder (Johns Hopkins University)
Topic: 
Conformal normal metrics with large Q-curvature

Abstract:
It is known that for a smooth non-constant non-positive function $f$ with  $\max f=0$ and for $\lambda>0$ small there exists a conformal metric on the 4-dimensional torus with Q-curvature  $f+\lambda$. The corresponding metrics exhibit a bubbling phenomena as $\lambda$ goes to zero. If all the maximum points of $f$ are non-degenerate, then after a suitable rescaling around a blow-up point $p$, the bubbling metrics converge to either a spherical metric or to a normal solution of $\Delta^2 u=(1+Hess(f)(p)[x,x])e^{4u}$ in $R^4$. I will talk about  existence and non-existence of solutions to the above equation. 

Event Date: 
September 29, 2020 - 10:30am to 11:20am
Location: 
Online
Calendar Category: 
Seminar
Seminar Category: 
Differential Geometry