Geodesic
Unique continuation properties for polyharmonic maps between Riemannian manifolds
Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 1-28

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DOI

Polyharmonic maps of order k (briefly, k-harmonic maps) are a natural generalization of harmonic and biharmonic maps. These maps are defined as the critical points of suitable higher-order functionals which extend the classical energy functional for maps between Riemannian manifolds. The main aim of this paper is to investigate the so-called unique continuation principle. More precisely, assuming that the domain is connected, we shall prove the following extensions of results known in the harmonic and biharmonic cases: (i) if a k-harmonic map is harmonic on an open subset, then it is harmonic everywhere; (ii) if two k-harmonic maps agree on an open subset, then they agree everywhere; and (iii) if, for a k-harmonic map to the n-dimensional sphere, an open subset of the domain is mapped into the equator, then all the domain is mapped into the equator.
DOI : 10.4153/S0008414X21000420
Mots-clés : polyharmonic maps, unique continuation principle, higher-order elliptic operators 
Branding, Volker; Montaldo, Stefano; Oniciuc, Cezar; Ratto, Andrea. Unique continuation properties for polyharmonic maps between Riemannian manifolds. Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 1-28. doi: 10.4153/S0008414X21000420
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     title = {Unique continuation properties for polyharmonic maps between {Riemannian} manifolds},
     journal = {Canadian journal of mathematics},
     pages = {1--28},
     year = {2023},
     volume = {75},
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     doi = {10.4153/S0008414X21000420},
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