F Functional and the First Eigenvalue for Quasi-Einstein Metrics

Qiao Fang Xing; Xiang Gao

doi:10.4028/www.scientific.net/AMM.475-476.1079

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 475-476F Functional and the First Eigenvalue for...

F Functional and the First Eigenvalue for Quasi-Einstein Metrics

Abstract:

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

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Periodical:

Applied Mechanics and Materials (Volumes 475-476)

Pages:

1079-1083

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.475-476.1079

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Online since:

December 2013

Authors:

Qiao Fang Xing, Xiang Gao*

Keywords:

Eigenvalue, F Functional, Laplacian Operator, Quasi-Einstein Metric, Ricci Flow

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* - Corresponding Author

References

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