Nonexistence of proper p-biharmonic maps and Liouville type theorems I: case of p = 2

摘要

Letu:(M,g)->(N,h) be a map between Riemannian manifolds (M, g) and (N, h). Thep-bienergy of u is defined by E-p(u) = integral(M)vertical bar tau(u)vertical bar(p)d nu(g), where tau(u) is the tension field of u and p > 1. Critical points of Ep(center dot) are called p-biharmonic maps. In this paper we will prove nonexistence result of proper p-biharmonic maps when p >= 2. In particular when M = R-m, we get Liouville type results under proper integral conditions , which extend the related results of Baird, Fardoun and Ouakkas (2010).