First eigenvalue estimates on complete balanced Hermitian manifolds

2025/11/03 by Zhang, Liangdi
#53C55 #58C40 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2511.01297

Abstract

In analogy with classical results in Riemannian geometry, we establish estimates for the first eigenvalue of the Laplace-de Rham operator on complete balanced Hermitian manifolds in terms of either the holomorphic Ricci curvature or the holomorphic sectional curvature associated with the Strominger-Bismut connection.

Citations

• Kählerness of compact Hermitian surfaces under semi-definite Strominger-Bismut-Ricci curvatures
• Chern number identities on compact complex surfaces and applications
• Comparison theorems in Hermitian geometry I
• First eigenvalue estimates on complete Kähler manifolds
• Rigidity results for non-Kähler Calabi-Yau geometries on threefolds
• The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound
• Bismut Einstein metrics on compact complex manifolds
• Bismut connection on Vaisman manifolds
• Eigenvalue estimates for Beltrami-Laplacian under Bakry-Émery Ricci curvature condition
• Pluriclosed and Strominger Kähler-like metrics compatible with abelian complex structures
• The Obata first eigenvalue theorems on a seven dimensional quaternionic\n contact manifold
• First Robin Eigenvalue of the p-Laplacian on Riemannian Manifolds
• Curvatures of real connections on Hermitian manifolds
• Ricci Curvatures on Hermitian manifolds
• Some Isoperimetric Inequalities and Eigenvalue Estimates in Weighted Manifolds
• Kahler manifolds with Ricci curvature lower bound
• Geometry of Hermitian manifolds
• On a characterization of the complex hyperbolic space
• A sharp estimate for the bottom of the spectrum of the Laplacian on Kähler manifolds
• Eigenfunction and Bochner Riesz estimates on manifolds with boundary
• Uniform bounds for eigenfunctions of the Laplacian on manifolds with boundary

Related

• First eigenvalue estimates on complete Kähler manifolds
• Total mean curvature and first Dirac eigenvalue
• Lower bounds for the first eigenvalue of the Laplacian on Kähler manifolds
• Eigenvalue estimates and applications on weighted manifolds
• Eigenvalue estimates of the Dirac operator depending on the Ricci tensor