Regularity of minimizing extrinsic polyharmonic maps in the critical dimension

Moser, Roger

doi:10.1007/s00229-010-0331-y

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…It asserts smoothness of biharmonic maps when the dimension n = 4, and the partial regularity of stationary biharmonic maps when n ≥ 5. Here we mention in passing the interesting works on biharmonic maps by Angelsberg [1], Strzelecki [31], Hong-Wang [17], Lamm-Rivière [24], Struwe [40], Ku [20], Gastel-Scheven [10], Scheven [34,35], Lamm-Wang [25], Moser [28,29], Gastel-Zorn [11], Hong-Yin [18], and Gong-Lamm-Wang [12]. Now we describe the initial and boundary value problem for the heat flow of biharmonic maps.…”

Section: Introductionmentioning

confidence: 99%

Regularity and uniqueness of a class of biharmonic map heat flows

2013

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In this paper, we first establish regularity of the heat flow of biharmonic maps into the unit sphere S L ⊂ R L+1 under a smallness condition of renormalized total energy. For the class of such solutions to the heat flow of biharmonic maps, we prove the properties of uniqueness, convexity of hessian energy, and unique limit at t = ∞. We also establish both regularity and uniqueness for the class of weak solutions u to the heat flow of biharmonic maps into any compact Riemannian manifold N without boundary such that ∇ 2 u ∈ L q t L p x for some p > n 2 and q > 2 satisfying (1.13). 7 2 ,2 (∂M, N ) (see [14]). Namely, there is a unique, global

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Section: Introductionmentioning

confidence: 99%

Regularity and uniqueness of a class of biharmonic map heat flows

2013

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“…For general (extrinsic) polyharmonic maps, Goldstein, Strzelecki and Zatorska-Goldstein [8] proved that a weakly polyharmonic map into sphere is smooth. For general target manifold, Moser [17] obtained the same result for energy minimizers using a flow method. It is completely solved in full generality by Gastel and Scheven [6].…”

Section: Introductionmentioning

confidence: 76%

Neck analysis of extrinsic polyharmonic maps

Yin

2017

Ann Glob Anal Geom

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“…It is likely that our approach, especially the general method to obtain strong energy quantization, applies to more general problem, as it was already shown in [26] in the case of p-harmonic maps. Furthermore, it is likely that it applies to polyharmonic maps in critical dimension too (see [8,32]), since one need only a Pohoazev identity, that always holds for such problems.…”

Section: New Developments In the Morse Index Stability And Future Workmentioning

confidence: 99%