2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102229Suppose $M$ 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.15 pagesDifferential Geometry58J35, 53C44,58C99text