info:eu-repo/semantics/article
The long-time behavior of the homogeneous pluriclosed flow
Fecha
2019-07Registro en:
Arroyo, Romina Melisa; Lafuente, Ramiro A.; The long-time behavior of the homogeneous pluriclosed flow; London Mathematical Society; Proceedings of the London Mathematical Society; 119; 1; 7-2019; 266-289
0024-6115
CONICET Digital
CONICET
Autor
Arroyo, Romina Melisa
Lafuente, Ramiro A.
Resumen
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.