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arXiv · 1712.02075

The long-time behavior of the homogeneous pluriclosed flow

Romina M. Arroyo·Ramiro A. Lafuente
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Abstract

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.

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Romina M. Arroyo, Ramiro A. Lafuente. 2017-12-06. The long-time behavior of the homogeneous pluriclosed flow. https://doi.org/10.1112/plms.12228

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