Rigidity properties of smooth metric measure spaces via the weighted -Laplacian
Author:
Nguyen Thac Dung
Journal:
Proc. Amer. Math. Soc. 145 (2017), 1287-1299
MSC (2010):
Primary 53C23, 53C24, 58J05
DOI:
https://doi.org/10.1090/proc/13285
Published electronically:
September 8, 2016
MathSciNet review:
3589326
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we show sharp estimates for the first eigenvalue of the weighted
-Laplacian on smooth metric measure spaces
. When the Bakry-Émery curvature
is bounded from below and the
weighted function is of sublinear growth, we prove some rigidity properties provided that the first eigenvalue
obtains its optimal value.
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Additional Information
Nguyen Thac Dung
Affiliation:
Department of Mathematics–Mechanics–Informatics (MIM), Hanoi University of Sciences (HUS-VNU), No. 334, Nguyen Trai Road, Thanh Xuan, Hanoi, Vietnam
Email:
dungmath@yahoo.co.uk, dungmath@gmail.com
DOI:
https://doi.org/10.1090/proc/13285
Keywords:
Weighted $p$-harmonic functions,
smooth metric measure spaces,
the first eigenvalue,
splitting theorems,
gradient Ricci solitons
Received by editor(s):
March 14, 2016
Received by editor(s) in revised form:
April 23, 2016, and May 4, 2016
Published electronically:
September 8, 2016
Communicated by:
Guofang Wei
Article copyright:
© Copyright 2016
American Mathematical Society