The Weierstrass representation of spheres in R, the Willmore numbers, and soliton spheres

In the present article we consider Weierstrass representations of spheres in R. An existence of a global Weierstrass representation for any compact oriented surface of genus g ≥ 1 has been established in [19, 20] and this proof, in fact, works for spheres also. Being mostly interested in relations of these representations to the spectral theory and in possibilities to apply the spectral theory to differential geometry ([17, 18]), we preferred to consider the case of spheres separately because in this case the spectral theory of Dirac operators