The long-time behavior of the homogeneous pluriclosed flow

ARROYO, ROMINA M.; LAFUENTE, RAMIRO A.

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

LONDON MATH SOC

Lugar: Londres; Año: 2019 vol. 119 p. 266 - 289

0024-6115

We study the asymptotic behavior of the pluriclosed flow in the case of left-invariant Hermitian structures on Lie groups. We prove that solutions on 2-step nilpotent Lie groups and on almost-abelian Lie groups converge, after a suitable normalization, to self-similar solutions of the flow. Given that the spaces are solvmanifolds, an unexpected feature is that some of the limits are shrinking solitons. We also exhibit the first example of a homogeneous manifold on which a geometric flow has some solutions with finite extinction time and some that exist for all positive times.