Riesz transform under perturbations via heat kernel regularity (Q2281149)

The main purpose of this paper is to study the behavior of the Riesz transform under metric perturbations in the abstract setting of complete, connected and non-compact \(n\)-dimensional Riemannian manifolds. As a byproduct, the authors also establish stability and instability of gradient estimates of harmonic functions and heat kernels under metric perturbation. Other related results in this paper include the case of degenerate elliptic equations on the whole space and remarks on the conic Laplace operators.