- Main
Generalized geometry and pluriclosed flow
- Jordan, Joshua Pierce
- Advisor(s): Streets, Jeffrey
Abstract
This dissertation will show the ways in which generalized geometry elucidates the study of pluriclosed flow. In their 2009 paper, Streets and Tian introduce pluriclosed flow -- a parabolic flow of pluriclosed metrics -- and classify some static solutions. In 2018, Streets expanded this into a geometrization conjecture for compact, complex surfaces. The author is able to use these tools to show an equivalence between pluriclosed flow and a non-linear, coupled Hermitian-Yang-Mills type flow. From there, the author is able to more geometrically prove a result of Streets and Warren -- an Evans-Krylov theorem for pluriclosed flow. The author is also able to use this equivalence to prove long-time existence and convergence of the flow on Bismut-flat manifolds and surfaces of non-negative Kodaira dimension.
Main Content
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