Finite time blowup of the n-harmonic flow on n-manifolds

Abstract

In this paper, we generalize the no-neck result of Qing and Tian (in Commun Pure Appl Math 50:295–310, 1997) to show that there is no neck during blowing up for the n-harmonic flow as $$t\rightarrow \infty $$ . As an application of the no-neck result, we settle a conjecture of Hungerbuhler (in Ann Scuola Norm Sup Pisa Cl Sci 4:593–631, 1997) by constructing an example to show that the n-harmonic map flow on an n-dimensional Riemannian manifold blows up in finite time for $$n\ge 3$$ .