Uniform Sobolev inequality along the Sasaki-Ricci flow

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.

13 pages

References in corpus (7)

• Canonical Sasakian Metrics
• The logarithmic Sobolev inequality along the Ricci flow
• Lectures on Stability and Constant Scalar Curvature
• Transverse Kähler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds
• Uniform Sobolev inequalities for manifolds evolving by Ricci flow
• The Transverse Entropy Functional and the Sasaki-Ricci Flow
• The Sasaki-Ricci flow and compact Sasakian manifolds of positive transverse holomorphic bisectional curvature