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Search: MSC category 53C44 ( Geometric evolution equations (mean curvature flow, Ricci flow, etc.) )

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1. CMB 2011 (vol 56 pp. 127)

Li, Junfang
Evolution of Eigenvalues along Rescaled Ricci Flow
In this paper, we discuss monotonicity formulae of various entropy functionals under various rescaled versions of Ricci flow. As an application, we prove that the lowest eigenvalue of a family of geometric operators $-4\Delta + kR$ is monotonic along the normalized Ricci flow for all $k\ge 1$ provided the initial manifold has nonpositive total scalar curvature.

Keywords:monotonicity formulas, Ricci flow
Categories:58C40, 53C44

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