Explicit lower bound of the first eigenvalue of the Laplacian on Kähler manifolds

Rutkowski, Benjamin; Seto, Shoo

doi:10.2140/involve.2023.16.519

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Explicit lower bound of the first eigenvalue of the Laplacian on Kähler manifolds

Benjamin Rutkowski and Shoo Seto

Vol. 16 (2023), No. 3, 519–527

DOI: 10.2140/involve.2023.16.519

Abstract

We establish an explicit lower bound of the first eigenvalue of the Laplacian on Kähler manifolds based off the comparison results of Li and Wang (Trans. Amer. Math. Soc. 374:11 (2021), 8081–8099). The lower bound will depend on the diameter, dimension, holomorphic sectional curvature and orthogonal Ricci curvature.

Keywords

Laplacian, eigenvalue, Kähler manifolds

Mathematical Subject Classification

Primary: 34L15, 53C55, 58C40

Milestones

Received: 27 June 2022

Accepted: 21 July 2022

Published: 10 August 2023

Communicated by Frank Morgan

Authors

Benjamin Rutkowski
Department of Mathematics California State University Fullerton, CA United States

Shoo Seto
Department of Mathematics California State University Fullerton, CA United States

Vol. 16, No. 3, 2023