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

Suppose M is a compact n-dimensional manifold, n≥ 2, with a metric g _ij (x, t) that evolves by the Ricci flow ∂ _t g _ij = −2R _ij in M× (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. Mathematics Subject Classification (1991) Primary 58J35, 53C44 Secondary 58C99