First eigenvalue of the $p$-Laplacian on K\"ahler manifolds

Casey Blacker; Shoo Seto

First eigenvalue of the $p$-Laplacian on K\"ahler manifolds

Differential Geometry 2018-09-12 v2

Authors: Casey Blacker , Shoo Seto

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.

Keywords

p-Laplacian Kähler manifold first eigenvalue Lichnerowicz bound Ricci curvature

Cite

@article{arxiv.1804.10876,
  title  = {First eigenvalue of the $p$-Laplacian on K\"ahler manifolds},
  author = {Casey Blacker and Shoo Seto},
  journal= {arXiv preprint arXiv:1804.10876},
  year   = {2018}
}

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