Regularity results for pluriclosed flow

Jeffrey Streets; Gang Tian

doi:10.2140/gt.2013.17.2389

Regularity results for pluriclosed flow

Jeffrey Streets, Gang Tian

Mathematics

Research output: Contribution to journal › Article › peer-review

56 Scopus citations

Abstract

In [27] 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.

Original language	English (US)
Pages (from-to)	2389-2429
Number of pages	41
Journal	Geometry and Topology
Volume	17
Issue number	4
DOIs	https://doi.org/10.2140/gt.2013.17.2389
State	Published - Aug 22 2013

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Geometric flow
Hermitian geometry

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10.2140/gt.2013.17.2389

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abstract = "In [27] 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{\"o}dinger 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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AB - In [27] 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.

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KW - Hermitian geometry

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JO - Geometry and Topology

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Regularity results for pluriclosed flow

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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