Regularity results for pluriclosed flow

TY - JOUR

T1 - Regularity results for pluriclosed flow

AU - Streets, Jeffrey

AU - Tian, Gang

PY - 2013/8/22

Y1 - 2013/8/22

N2 - 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.

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.

KW - Geometric flow

KW - Hermitian geometry

UR - https://www.scopus.com/pages/publications/84883139048

UR - https://www.scopus.com/pages/publications/84883139048#tab=citedBy

U2 - 10.2140/gt.2013.17.2389

DO - 10.2140/gt.2013.17.2389

M3 - Article

SN - 1465-3060

VL - 17

SP - 2389

EP - 2429

JO - Geometry and Topology

JF - Geometry and Topology

IS - 4

ER -