A sharp stability estimate in tensor tomography

TL;DR

This paper establishes a precise stability estimate for reconstructing symmetric 2-tensors from geodesic integrals on simple manifolds, advancing the mathematical understanding of tensor tomography.

Contribution

It provides the first sharp stability estimate for tensor tomography on simple manifolds, improving previous bounds and theoretical understanding.

Findings

Proved a sharp stability estimate for tensor reconstruction.

Enhanced theoretical bounds for tensor tomography.

Improved understanding of the stability in tensor integral problems.

Abstract

We prove a sharp stability estimate for the problem of reconstructing a symmetric 2-tensor from its integrals along all maximal geodesics on a simple manifold.