Evolution of the first eigenvalue of the clamped plate on manifold along the Ricci flow

ABSTRACT

In this article, we study the evolution, monotonicity for the first eigenvalue of the clamped plate on closed Riemannian manifold along the Ricci flow. We prove that the first nonzero eigenvalue is nondecreasing under the Ricci flow under certain geometric conditions and find some applications in 2-dimensional manifolds.

COMMUNICATED BY:

• Y. Antipov

KEYWORDS:

• Laplace
• Ricci flow
• eigenvalue

AMS SUBJECT CLASSIFICATIONS:

• 58C40
• 53C44
• 53C21

Disclosure statement

No potential conflict of interest was reported by the author.