College of Liberal Arts & Sciences
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