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arXiv · 1708.08571

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

Leslie Hon-Nam Cheung·Min-Chun Hong
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Abstract

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 $n\geq 3$.

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Leslie Hon-Nam Cheung, Min-Chun Hong. 2017-08-29. Finite time blowup of the $n$-harmonic flow on $n$-manifolds. https://arxiv.org/abs/1708.08571

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