Regularity results for pluriclosed flow

By Jeffrey Streets, G. Tian. 2010

136 citations recorded by the source corpus.

In prior work the authors introduced a parabolic flow of pluriclosed metrics. Here we give improved regularity results for solutions to this equation. Furthermore, we exhibit this equation as the gradient flow of the lowest eigenvalue of a certain Schr\"odinger operator, and show the existence of an expanding entropy functional for this flow. Finally, we motivate a conjectural picture of the optimal regularity results for this flow, and discuss some of the consequences.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c434f5b91b3133b35bd71f418ce86d936cfd531

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On Bismut flat manifolds (2016, unknown): “We refer the readers to [37], [9], [10], [11], [12], [13], [24], [41], [19], [16], [17], [18], [33], [34], [35], [36], [25], [26], [27], [39], [40], [38] and the references therein for some recent progress in this area.”
Ricci Curvatures on Hermitian manifolds (2014, methodology): “[45, 46, 47], [39], [24, 51, 52, 55, 25, 26]) by using the well-studied Hamilton’s Ricci flow.”
The long‐time behavior of the homogeneous pluriclosed flow (2017, background): “In recent years, the pluriclosed flow has been an active subject of study, and already many regularity and convergence results have been established [29, 33], as well as connections with generalized Kähler geometry [32].”
On the evolution of a Hermitian metric by its Chern-Ricci form (2011, background): “4 were conjectured by Streets-Tian [44] for their pluriclosed flow (see Section 2 below).”
Strominger connection and pluriclosed metrics (2019, methodology): “We refer the readers to the papers [8], [13], [14], [16], [26], [39] for study involving Hull-Strominger system, which uses Bismut-Strominger connection in an essential way, and to the papers [33], [34], [35] where the study of Hermitian curvature flow involving the connection were initiated which h”