Evolution of Eigenvalues along Rescaled Ricci Flow

Canadian mathematical bulletin

Junfang Li¹ 

[1] Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294

关键词: monotonicity formulas;    Ricci flow;   

DOI  :  10.4153/CMB-2011-162-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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

【 授权许可】

Unknown