Abstract:
In this paper, we generalize the no-neck result of Qing-Tian \cite{QT} to show that there is no neck during blowing up for the $n$-harmonic flow as $t\to\infty$. As an application of the no-neck result, we settle a conjecture of Hungerb\"uhler \cite {Hung} by constructing an example to show that the $n$-harmonic map flow on an $n$-dimensional Riemannian manifold blows up in finite time for $n\geq 3$. (This is my joint work with Leslie Cheung).
Biography:
Min-Chun Hong obtained both of his BSc and MSc from Nankai University in 1983 and 1986, respectively. He received his Ph.D. from Zhejiang University in 1988. His research interests are in non-linear partial differential, equations, geometric analysis and calculus of variations.