Work

Spectral Improvements of Geometric Inequalities on Closed Kähler Manifolds

Year: 2026

Type: preprint

Abstract: Let $(M,g,J)$ be a closed Kähler manifold satisfying $\operatorname{Ric}\geqslant g$. We establish improved Liouville theorems for the Euler--Lagrange equations associated with the Beckner--Sobolev inequalities by incorporating the first positive eigenvalue of the $\bar\partial$-Laplacian into a differential-identity argument. As a consequence, we obtain improved Sobolev and Beckner inequalities that refine the known Riemannian and Kähler estimates when the first eigenvalue is sufficiently large. We also derive new upper bounds for the diameter of $(M,g)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.03287

Authors: Chakraborty, Sayantan, Wang, Xiaodong, Wu, Tian

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Central China Normal University, Fundamental Research Funds for the Central Universities, Division of Mathematical Sciences

Award: G5070767354

OpenAlex ID: W7208716160

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