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

Nguyen Thac Dung | Zendy

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

Author(s) -

Nguyen Thac Dung

Publication year - 2016

Publication title -

proceedings of the american mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.968

H-Index - 84

eISSN - 1088-6826

pISSN - 0002-9939

DOI - 10.1090/proc/13285

Subject(s) - rigidity (electromagnetism) , measure (data warehouse) , mathematics , laplace operator , metric space , metric (unit) , pure mathematics , mathematical analysis , computer science , physics , data mining , engineering , operations management , quantum mechanics

In this paper, we show sharp estimates for the first eigenvalue λ 1 , p \lambda _{1, p} of the weighted p p -Laplacian on smooth metric measure spaces ( M , g , e − f d v ) (M, g, e^{-f}dv) . When the Bakry-Émery curvature R i c f Ric_f is bounded from below and the weighted function f f is of sublinear growth, we prove some rigidity properties provided that the first eigenvalue λ 1 , p \lambda _{1, p} obtains its optimal value.

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