Volume 17, issue 4 (2013)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Regularity results for pluriclosed flow

Jeffrey Streets and Gang Tian

Geometry & Topology 17 (2013) 2389–2429
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/