Uniform Sobolev inequality along the Sasaki-Ricci flow

TL;DR

This paper establishes a uniform Sobolev inequality along the Sasaki-Ricci flow, introducing new function space theory and heat kernel decomposition results on Sasaki manifolds.

Contribution

It develops the theory of basic Lebesgue and Sobolev spaces and proves heat kernel decomposition results, enabling the proof of the uniform Sobolev inequality.

Findings

Proved a uniform Sobolev inequality along the Sasaki-Ricci flow.

Developed the theory of basic Lebesgue and Sobolev spaces on Sasaki manifolds.

Established general results on heat kernel decomposition for elliptic operators.

Abstract

We prove a uniform Sobolev inequality along the Sasaki-Ricci flow. In the process, we develop the theory of basic Lebesgue and Sobolev function spaces, and prove some general results about the decomposition of the heat kernel for a class of elliptic operators on a Sasaki manifold.