Monotonicity of Eigenvalues and Certain Entropy Functional under the Ricci Flow
نویسنده
چکیده
Geometric monotone properties of the first nonzero eigenvalue of Laplacian form operator under the action of the Ricci flow in a compact nmanifold ( ) 2 ≥ n are studied. We introduce certain energy functional which proves to be monotonically non-decreasing, as an application, we show that all steady breathers are gradient steady solitons, which are Ricci flat metric. The results are also extended to the case of normalized Ricci flow, where we estabilish non-existence of expanding breathers other than gradient solitons.
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