Monotonicity Properties of the First Eigenvalue of the Laplacian Operator on Ricci Solitons

Authors

  • Xiang Gao School of Mathematical Sciences, Ocean University of China, Lane 238, Songling Road, Laoshan District, Qingdao City, Shandong Province, 266100, People's Republic of China
  • Qiaofang Xing Institute of Science, Information Engineering University, Zhengzhou City, Henan Province, 450001, People's Republic of China

DOI:

https://doi.org/10.26713/jims.v4i2.85

Keywords:

Laplacian operator, Ricci soliton, $\mathcal{F}$ functional

Abstract

In this paper, we deal with the monotonicity properties of the first eigenvalue of the Laplacian operator on Ricci solitons. Firstly, by using the monotonicity formula of the $\mathcal{F}$ functional, we derive a monotonicity formula of the first eigenvalue of the Laplacian operator on Ricci solitons. Based on this, we also prove an exponential decreasing property of the first eigenvalue.
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Issue

Vol. 4 No. 2 (2012)

Section

Research Article

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How to Cite

Gao, X., & Xing, Q. (2012). Monotonicity Properties of the First Eigenvalue of the Laplacian Operator on Ricci Solitons. Journal of Informatics and Mathematical Sciences, 4(2), 219-227. https://doi.org/10.26713/jims.v4i2.85