Work

First Robin Eigenvalue of the Laplacian on Kähler and Quaternionic Kähler Manifolds

Year: 2025

Type: article

Abstract: We investigate the first Robin eigenvalue of the Laplacian on Kähler and quaternionic Kähler manifolds. First, we establish Cheng-type eigenvalue comparison theorems for Kähler manifolds under lower bounds on holomorphic sectional curvature and orthogonal Ricci curvature and for quaternionic Kähler manifolds under scalar curvature lower bounds. For compact Kähler and quaternionic Kähler manifolds, our second result derives lower bounds for the first Robin eigenvalue when the Robin parameter α is positive, with corresponding upper bounds when it is negative.

Source: Mathematics

DOI: 10.3390/math13243970

Authors: Shaoheng Zhang, Weijie Zhu

Institution: Soochow University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Government of Jiangsu Province