Eigenfunctions of the weighted Laplacian and a vanishing theorem on gradient steady Ricci soliton

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Nguyen Thac Dung¹  Nguyen Thi Le Hai²  Nguyen Thi Thanh³ 

[1] Hanoi Univ Sci, Dept Math Mech & Informat MIM, Hanoi, Vietnam

[2] Hanoi Univ Civil Engn, Dept Informat Technol, Hanoi, Vietnam

[3] Tran Phu High Sch Gifted, Hai Phong City, Vietnam

关键词: Bakry-Emery curvature;    Eigenvalues;    Eigenfunctions;    Gradient steady Ricci soliton;    Smooth metric measure spaces;   

DOI  :  10.1016/j.jmaa.2014.02.054

来源: Elsevier

【 摘 要 】

The aim of this note has two folds. First, we show a gradient estimate of the higher eigenfunctions of the weighted Laplacian on smooth metric measure spaces. In the second part, we consider a gradient steady Ricci soliton and prove that there exists a positive constant c(n) depending only on the dimension n of the soliton such that there is no nontrivial harmonic 1-form (hence harmonic function) which is in L-P on such a soliton for any 2 < c(n). (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free