On the explicit reconstruction of a Riemann surface from its Dirichlet-Neumann operator

Gennadi Henkin (1) , Vincent Michel (1)

1 IMJ - Institut de Mathématiques de Jussieu

This article gives a complex analysis lighting on the problem which consists in restoring a bordered connected riemaniann surface from its boundary and its Dirichlet-Neumann operator. The three aspects of this problem, unicity, reconstruction and characterization are approached.

Mots clés: Dirichlet-Neumann operator; EIT; Plateau problem

Domaines: Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]; Analyse classique [math.CA]

Gennadi Henkin, Vincent Michel. On the explicit reconstruction of a Riemann surface from its Dirichlet-Neumann operator. 2005. ⟨hal-00004910v6⟩