A response to an article of Xu-Jia Wang

TL;DR

This paper critically responds to Xu-Jia Wang's article, highlighting unresolved objections and identifying fundamental errors regarding superharmonic functions in the context of conformal Laplacians.

Contribution

It clarifies the authors' original objections and exposes a significant mathematical mistake in Wang's paper concerning superharmonic functions.

Findings

Wang's article does not address the raised objections.

Identification of a false assertion about superharmonic functions.

Highlighting serious mathematical errors in Wang's work.

Abstract

This is a response to the article arXiv:1212.3130v1 by Xu-Jia Wang, where he attempted to address a mathematical question we raised. We point out that, and explain why, the article is far from answering our objections. Moreover, we have more recently found more serious trouble in the paper under discussion based on the false assertion there that minimal radial functions of superharmonic functions (with respect to a conformal Laplacian of a Riemannian metric) are superharmonic.