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Energy convexity of intrinsic bi-harmonic maps and applications I: Spherical target
Journal für die reine und angewandte Mathematik ( IF 1.486 ) Pub Date : 2020-09-11 , DOI: 10.1515/crelle-2020-0028
Paul Laurain; Longzhi Lin

In this paper, we show an energy convexity and thus uniqueness for weakly intrinsic bi-harmonic maps from the unit 4-ball B14 into the sphere 𝕊n. In particular, this yields a version of uniqueness of weakly harmonic maps on the unit 4-ball which is new. We also show a version of energy convexity along the intrinsic bi-harmonic map heat flow into 𝕊n, which in particular yields the long-time existence of the intrinsic bi-harmonic map heat flow, a result that was until now only known assuming the non-positivity of the target manifolds by Lamm []. Further, we establish the previously unknown result that the energy convexity along the flow yields uniform convergence of the flow.
更新日期:2020-09-18

 

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