Hamiltonian structure of the harmonic functions on an annulus

J. Muñoz Masqué

Instituto de Física Aplicada, CSIC C/ Serrano 144, 28006-Madrid, Spain

                 E-mail: jaime@iec.csic.es

L.M. Pozo Coronado

Departamento de Geometría y Topología Universidad Complutense de Madrid, 28040-Madrid, Spain

                E-mail: luispozo@mat.ucm.es

Abstract

We consider the space of harmonic functions on an n-dimensional annulus, seen as the space of extremals of the energy functional. The variational approach allows us to find an alternate bilinear form which is proved to be nondegenerate, thus endowing the harmonic functions with an structure of a symplectic manifold.