Regularity results for pluriclosed flow

Details Regularity results for pluriclosed flow Regularity results for pluriclosed flow

2010-08-16

arxiv.org/abs/1008.2794v1

Mathematics

Differential Geometry

Scientific paper

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.

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