A simple proof on the non-existence of shrinking breathers for the Ricci flow

Shu-Yu Hsu

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A simple proof on the non-existence of shrinking breathers for the Ricci flow

Shu-Yu Hsu

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Abstract

Suppose $M$ is a compact n-dimensional manifold, $n\ge 2$, with a metric $g_{ij}(x,t)$ that evolves by the Ricci flow $\partial_tg_{ij}=-2R_{ij}$ in $M\times (0,T)$. We will give a simple proof of a recent result of Perelman on the non-existence of shrinking breather without using the logarithmic Sobolev inequality.

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Shu-Yu Hsu. 2006-01-21. A simple proof on the non-existence of shrinking breathers for the Ricci flow. https://arxiv.org/abs/math/0509087

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