75 citations · 334 across the 43 of their papers we have counts for
4 papers · 1 filter
On the convergence of the Sasaki-Ricci flow
Tristan C. Collins, Adam Jacob
Given a Sasaki manifold S, we prove the Sasaki-Ricci flow converges exponentially fast to a Sasaki-Einstein metric if one exists, provided the automorphism group of the transverse…
Stability and Convergence of the Sasaki-Ricci Flow
Tristan C. Collins
We introduce a holomorphic sheaf E on a Sasaki manifold and study two new notions of stability for E along the Sasaki-Ricci flow related to the `jumping up' of the number of global…
Uniform Sobolev inequality along the Sasaki-Ricci flow
Tristan C. Collins
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 resul…
The Transverse Entropy Functional and the Sasaki-Ricci Flow
Tristan C. Collins
We introduce two new functionals on Sasaki manifolds, inspired by the work of Perelman, which are monotonic along the Sasaki-Ricci flow. We relate their gradient flow, via diffeomo…