A remark on inverse problems for nonlinear magnetic Schr\"odinger equations on complex manifolds

TL;DR

This paper proves that the boundary data for a nonlinear magnetic Schrödinger equation on certain complex manifolds uniquely determines the magnetic and electric potentials, advancing inverse problem theory in complex geometry.

Contribution

It establishes a uniqueness result for inverse boundary value problems for nonlinear magnetic Schrödinger equations on complex manifolds with Kähler metrics.

Findings

Unique determination of magnetic and electric potentials from boundary data

Results apply to manifolds with sufficient global holomorphic functions

Advances understanding of inverse problems in complex geometric settings

Abstract

We show that the knowledge of the Dirichlet--to--Neumann map for a nonlinear magnetic Schr\"odinger operator on the boundary of a compact complex manifold, equipped with a K\"ahler metric and admitting sufficiently many global holomorphic functions, determines the nonlinear magnetic and electric potentials uniquely.