A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies
نویسندگان
چکیده
منابع مشابه
A Short Survey on Biharmonic Maps between Riemannian Manifolds
and the corresponding Euler-Lagrange equation is H = 0, where H is the mean curvature vector field. If φ : (M, g) → (N, h) is a Riemannian immersion, then it is a critical point of the bienergy in C∞(M,N) if and only if it is a minimal immersion [26]. Thus, in order to study minimal immersions one can look at harmonic Riemannian immersions. A natural generalization of harmonic maps and minimal ...
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(0.1) i) φ ∈ C1((0,+∞)) ∩ C0([0,+∞)); ii) φ(0) = 0, φ(t) > 0 on (0,+∞); iii) φ(t) ≤ Atδ on [0,+∞) for some constants A, δ > 0. We state our main result in the form of the following Liouville type: Theorem A. Let (M, 〈〉), r(x) be as above and let φ satisfy (0.1). Let u ∈ C2(M) be a solution of the equation (0.2) div (|∇u|−1 φ(|∇u|)∇u) = a for some a ∈ R, such that (0.3) u(x) = o ( log r(x) ...
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ژورنال
عنوان ژورنال: Archiv der Mathematik
سال: 2018
ISSN: 0003-889X,1420-8938
DOI: 10.1007/s00013-018-1189-6