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 monotonicity formulas, Ricci flow

MSC Classifications:

58C40, 53C44 show english descriptions Spectral theory; eigenvalue problems [See also 47J10, 58E07]
Geometric evolution equations (mean curvature flow, Ricci flow, etc.) 58C40 - Spectral theory; eigenvalue problems [See also 47J10, 58E07]
53C44 - Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

top of page | contact us | social media | privacy | site map