Invariant distributions and tensor tomography for Gaussian thermostats

TL;DR

This paper investigates the properties of the Gaussian thermostat ray transform on Riemannian surfaces, focusing on its injectivity and the surjectivity of its adjoint, which are key for understanding inverse problems in geometric analysis.

Contribution

The paper provides new results on the injectivity and surjectivity of the Gaussian thermostat ray transform on both closed and bounded Riemannian surfaces.

Findings

Injectivity results for the thermostat ray transform

Surjectivity of the adjoint transform established

Applicable to both closed and boundary Riemannian surfaces

Abstract

In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the surjectivity of its adjoint.