First eigenvalue of the $p$-Laplacian on Kähler manifolds

Casey Blacker,Shoo Seto

doi:10.1090/proc/14395

First eigenvalue of the $p$-Laplacian on Kähler manifolds

Casey Blacker, Shoo Seto

Open Access

https://doi.org/10.1090/proc/14395

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Journal: Proceedings of the American Mathematical Society	Publication Date: Jan 18, 2019
Citations: 20	License type: publisher-specific, author manuscript

Affiliation: University of California, Santa Barbara

#Ahler Manifolds #Positive Ricci Curvature + Show 4 more

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Abstract

We prove a Lichnerowicz type lower bound for the first nontrivial eigenvalue of the $p$-Laplacian on K\"ahler manifolds. Parallel to the $p = 2$ case, the first eigenvalue lower bound is improved by using a decomposition of the Hessian on K\"ahler manifolds with positive Ricci curvature.

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