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

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

2005-09-05

arxiv.org/abs/math/0509087v2

Mathematics

Differential Geometry

15 pages

Scientific paper

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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