English

Eigenvalues under the Ricci flow of model geometries

Differential Geometry 2019-08-13 v2

Abstract

In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized Ricci flow of model geometries. In every Bianchi class, we estimate the derivative of the eigenvalue. Then we construct monotonic quantities under the Ricci flow and obtain upper and lower bounds for the eigenvalue.

Keywords

Cite

@article{arxiv.1602.04597,
  title  = {Eigenvalues under the Ricci flow of model geometries},
  author = {Songbo Hou},
  journal= {arXiv preprint arXiv:1602.04597},
  year   = {2019}
}

Comments

15 pages

R2 v1 2026-06-22T12:50:12.500Z