Andrea Ratto

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.

Biharmonic Functions on the Classical Compact Simple Lie Groups

The main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups

On cohomogeneity one biharmonic hypersurfaces into the Euclidean space

\mathbf{SU}(n)

Proper biconservative immersions into the Euclidean space

SU(n),

Rotationally symmetric biharmonic maps between models

\mathbf{SO}(n)

A generalisation of the Hopf construction and harmonic morphisms into {\mathbb {S}^2}

SO(n) and