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arXiv · 1908.05410

On the long-time behavior of immortal Ricci flows

Shaosai Huang
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Abstract

For an immortal Ricci flow on an $m$-dimensional $(m\ge 3)$ closed manifold, we show the following convergence results: (1) if the curvature and diameter are uniformly bounded, then any unbounded sequence of time slices sub-converges to a Riemannian orbifold; (2) if the flow is type-III with diameter growth controlled by $t^{\frac{1}{2}}$, then any blowdown limit is an $m$-dimensional negative Einstein manifold, provided that Feldman-Ilmanen-Ni's $\boldsymbol{\mu}_+$-functional satisfies $\lim_{t\to \infty} t\boldsymbol{\mu}_+'(t)=0$.

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Shaosai Huang. 2019-08-15. On the long-time behavior of immortal Ricci flows. https://arxiv.org/abs/1908.05410

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