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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
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