Anisotropic Calder\'{o}n problem of a nearly Laplace-Beltrami operator of order $2+$

TL;DR

This paper studies the anisotropic Calderón problem for a nearly Laplace-Beltrami operator on closed Riemannian manifolds, showing that the Cauchy data set determines the manifold's geometry up to gauge.

Contribution

It extends the Calderón problem to a logarithmic Laplacian, providing new insights into inverse problems for nearly Laplace operators on manifolds.

Findings

Cauchy data set recovers manifold geometry up to gauge

Extension of Calderón problem to logarithmic Laplacian

Results applicable to closed Riemannian manifolds

Abstract

This paper investigates the anisotropic Calder\'{o}n problem for Logarithemic Laplacian, on closed Riemannian manifolds, which could be considered as near Laplace operator. We demonstrate that the Cauchy data set recovers the geometry of a closed Riemannian manifold up to standard gauge.