A general approach to equivariant biharmonic maps
  In this paper we describe a 1-dimensional variational approach to the analytical construction of equivariant biharmonic maps. Our goal is to provide a direct method which enables analysts to compute directly the analytical conditions which guarantee biharmonicity in the presence of suitable symmetries. In the second part of our work, we illustrate and discuss some examples. In particular, we obtain a 1-dimensional stability result, and also show that biharmonic maps do not satisfy the classical maximum principle proved by Sampson for harmonic maps. 
Stefano Montaldo, Andrea Ratto
math.DG