弱Kähler双曲流形与Green--Griffiths--Lang猜想
Weakly Kähler hyperbolic manifolds and the Green--Griffiths--Lang conjecture
AI总结：
本文引入弱Kähler双曲流形概念，证明其谱间隙与一般型性质，并验证Lang和Green--Griffiths猜想的相关方面。
摘要：
我们引入了弱Kähler双曲流形的概念，它推广了M. Gromov在90年代初提出的Kähler双曲流形，并建立了其基本性质。随后我们研究了其谱性质，并在适当的修改上证明了谱间隙结果。作为应用，我们证明了弱Kähler双曲流形属于一般型，并研究了其子簇和整曲线的几何，从而验证了这类流形的Lang猜想和Green--Griffiths猜想的多个方面。
英文摘要：
We introduce the notion of weakly Kähler hyperbolic manifold which generalizes that of Kähler hyperbolic manifold given in the early '90s by M. Gromov, and establish its basic features. We then investigate its spectral properties and show a spectral gap result (on a suitable modification). As applications, we prove that weakly Kähler hyperbolic manifolds are of general type and we study the geometry of their subvarieties and entire curves, verifying -- among other things -- various aspects of the Lang and the Green--Griffiths conjectures for this class of manifolds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
