English

General estimate of the first eigenvalue on manifolds

Probability 2011-11-30 v1 Differential Geometry Spectral Theory

Abstract

Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on compact Riemannian manifolds are reviewed and compared. An improved variational formula, a general common estimate, and a new sharp one are added. The best lower estimates are now updated. The new estimates provide a global picture of what one can expect by our approach.

Keywords

Cite

@article{arxiv.1111.6663,
  title  = {General estimate of the first eigenvalue on manifolds},
  author = {Mu-Fa Chen},
  journal= {arXiv preprint arXiv:1111.6663},
  year   = {2011}
}

Comments

19 pages

R2 v1 2026-06-21T19:42:57.145Z