1. CMB 2011 (vol 56 pp. 127)
|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