Regularity results for pluriclosed flow

Streets, Jeffrey; Tian, Gang

doi:10.2140/gt.2013.17.2389

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Regularity results for pluriclosed flow

Jeffrey Streets and Gang Tian

Geometry & Topology 17 (2013) 2389–2429

DOI: 10.2140/gt.2013.17.2389

Abstract

In [Int. Math. Res. Not. 16 (2010) 3101–3133] 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 Schrödinger 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.

Keywords

geometric flow, Hermitian geometry

Mathematical Subject Classification 2010

Primary: 32Q55, 53C44, 53C55

References

Publication

Received: 1 March 2013

Accepted: 29 May 2013

Published: 22 August 2013

Proposed: Tom Mrowka

Seconded: Tobias Colding, Ronald Stern

Authors

Jeffrey Streets
Department of Mathematics University of California, Irvine Rowland Hall Irvine, CA 92617 USA

Gang Tian
Department of Mathematics Princeton University Fine Hall Princeton, NJ 08544 USA
http://www-math.mit.edu/~tian/

Volume 17, issue 4 (2013)