Subelliptic operators on weighted Folland-Stein spaces

TL;DR

This paper proves that the sub-Laplacian on certain weighted Folland-Stein spaces is an isomorphism, resolving key problems in CR geometry such as the CR positive mass and Yamabe problems.

Contribution

It establishes the isomorphism property of the sub-Laplacian on weighted Folland-Stein spaces, leading to solutions of fundamental CR geometric problems.

Findings

Sub-Laplacian is an isomorphism on weighted Folland-Stein spaces.

CR positive mass problem is resolved.

CR Yamabe problem is addressed.

Abstract

In this paper, we show that the sub-Laplacian of an asymptotically flat pseudo-hermitian manifold defined on a suitable weighted Folland-Stein spaces is an isomorphism. It turns out that the CR positive mass problem is resolved, and hence CR Yamabe problem.