Injectivity of the Dirichlet-to-Neumann Functional and the Schwarzian Derivative

ABSTRACT

In this article, we show the relation between the Schwartz kernels of the Dirichlet-to-Neumann operators associated to the metrics g0 and h = F* (e²φ g0) on the circular annulus A R, and the Schwarzian Derivative of the argument function f of the restriction of the diffeomorphism F to the boundary of A R.

RESUMO

Neste artigo mostramos a relação entre os núcleos de Schwartz dos operadores Dirichlet-to-Neumann associados à métrica g0 e h = F* (e²φ g0), no anel circular A R, e a Derivada Schwarziana da função argumento f, da restrição do difeomorfismo F à fronteira de A R.