Immortal homogeneous Ricci flows

2017/01/31 by Christoph Böhm, Ramiro A. Lafuente · 1 citation
Mathematics · #math.DG #msc:53C44 #msc:53C30

paper · pdf · doi:10.1007/s00222-017-0771-z

Final version, to appear in Invent. Math

arxiv created 2017/11/17 · arxiv updated 2018/05/09

Abstract

We show that for an immortal homogeneous Ricci flow solution any sequence of parabolic blow-downs subconverges to a homogeneous expanding Ricci soliton. This is established by constructing a new Lyapunov function based on curvature estimates which come from real geometric invariant theory.

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• Homogeneous spaces with two equivalent isotropy summands develop positive Ricci curvature under Ricci flow

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