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

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Abstract

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.

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Correspondence to Shu-Yu Hsu.

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Mathematics Subject Classification (1991) Primary 58J35, 53C44 Secondary 58C99

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Hsu, SY. A simple proof on the non-existence of shrinking breathers for the Ricci flow. Calc. Var. 27, 59–73 (2006). https://doi.org/10.1007/s00526-006-0023-3

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