Article citationsMore>>

Bracken, P. (2017) An Introduction to the Ricci Flow for Two-Dimensional Manifolds, Advances in Mathematics Research. Nova Science Publishers, Hauppauge, NY, 155-163.

has been cited by the following article:

• TITLE: Evolution of the First Eigenvalue of a (p,q)-Laplacian Under a Harmonic Ricci Flow

  AUTHORS: Paul Bracken

  KEYWORDS: Ricci Flow, Curvature, Eigenvalue, Evolution, Laplacian, Nonlinear

  JOURNAL NAME: Advances in Pure Mathematics, Vol.11 No.4, April 6, 2021

  ABSTRACT: The properties of the first eigenvalue of a class of (p,q) Laplacian are investigated. A variational formulation for the first eigenvalue of the Laplacian on a closed Riemannian manifold is obtained. This eigenvalue corresponds to a nonlinear, coupled system of p-Laplacian partial differential equations. The main idea is to investigate the evolution of the first eigenvalue of the system under the Ricci harmonic flow. It is also possible to construct monotonic quantities based on them and study their evolution which is done.