Rigidity properties of smooth metric measure spaces via the weighted 𝑝-Laplacian

Dung, Nguyen Thac

doi:10.1090/proc/13285

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
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Abstract: In this paper, we show sharp estimates for the first eigenvalue $\lambda _{1, p}$ of the weighted -Laplacian on smooth metric measure spaces $(M, g, e^{-f}dv)$ . 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 $\lambda _{1, p}$ obtains its optimal value.

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