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 $p$-Laplacian
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Proc. Amer. Math. Soc. 145 (2017), 1287-1299 Request permission

Abstract:

In this paper, we show sharp estimates for the first eigenvalue $\lambda _{1, p}$ of the weighted $p$-Laplacian on smooth metric measure spaces $(M, g, e^{-f}dv)$. When the Bakry-Émery curvature $Ric_f$ is bounded from below and the weighted function $f$ 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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