The long‐time behavior of the homogeneous pluriclosed flow

By Romina M. Arroyo, Ramiro A. Lafuente. Proceedings of the London Mathematical Society, 2017

51 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/35324a7fd792c2c50780a5f420df7944ccf1c404

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Non-Kähler Calabi-Yau geometry and pluriclosed flow (2021, background): “Global existence and convergence results in various geometric settings have appeared in [6, 7, 8, 13, 23, 52, 53, 54].”
Balanced Hermitian structures on almost abelian Lie algebras (2020, methodology): “, e2n}, so that, by [6], the corresponding data (a, v, A) in (2.”