Inverse conductivity problem on a Riemann surface

TL;DR

This paper applies advanced integral formulas and boundary maps to solve the inverse conductivity problem on bordered Riemann surfaces, extending techniques from complex analysis to geometric inverse problems.

Contribution

It introduces a novel approach combining the Faddeev-Henkin exponential ansatz and boundary d-to-d-bar maps for inverse conductivity on Riemann surfaces.

Findings

Successfully extends inverse conductivity methods to Riemann surfaces

Utilizes integral formulas for d-bar operators and holomorphic functions

Provides a framework for boundary-based inverse problems on complex manifolds

Abstract

We present an application of the Faddeev-Henkin exponential ansatz and of the d-to-d-bar map on the boundary to inverse conductivity problem on a bordered Riemann surface in CP2. In our approach we use integral formulas for operator d-bar developed in [HP1]-[HP4] and integral formulas for holomorphic functions on Riemann surfaces from [P].