# Inverse conductivity problem in dimension two

## TL;DR

This paper presents a method to reconstruct a Riemann surface with boundary and conductivity tensor from boundary measurements, enabling the recovery of all information obtainable from such data in two dimensions.

## Contribution

It introduces a process to reconstruct the entire Riemann surface and conductivity tensor from boundary data in two dimensions, advancing inverse boundary value problem solutions.

## Key findings

- Successful reconstruction of Riemann surfaces with boundary from boundary data.
- Complete recovery of the conductivity tensor and surface geometry from Dirichlet-Neumann data.
- Applicable to two-dimensional real Riemannian surfaces with boundary.

## Abstract

This article proposes a process to reconstruct a Riemann surface with boundary equipped with a conductivity tensor from its boundary and its Dirichlet-Neumann operator. When initial data comes from a two dimensional real Riemannian oriented surface equipped with a conductivity tensor, this process recover the whole of what can be determined from this data.