Some Asymptotic Behavior of the first Eigenvalue along the Ricci Flow
Jun Ling
TL;DR
This paper investigates the long-term behavior of the first nonzero eigenvalue of the Laplacian during the normalized Ricci flow, providing a concise proof for its asymptotic upper limit estimate.
Contribution
It offers a new, direct proof for the asymptotic upper limit estimate of the first eigenvalue along the Ricci flow.
Findings
Established an asymptotic upper limit for the first eigenvalue
Provided a simplified proof technique
Enhanced understanding of spectral behavior under Ricci flow
Abstract
We study some asymptotic behavior of the first nonzero eigenvalue of the Lalacian along the normalized Ricci flow and give a direct short proof for an asymptotic upper limit estimate.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations