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

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 → ∞ . As an application of the no-neck result, we settle a conjecture of Hungerbühler (in Ann Scuola Norm Sup Pi...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2018-02, Vol.57 (1), p.1-24, Article 9
Main Authors: Cheung, Leslie Hon-Nam, Hong, Min-Chun
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Flow mapping
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Riemann manifold
Systems Theory
Theoretical
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Summary: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 → ∞ . As an application of the no-neck result, we settle a conjecture of Hungerbühler (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 ≥ 3 .
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-017-1282-x