论文标题
谐波形式，最小表面和关于双曲线$ 3 $ MANIFOLDS的共同体学规范
Harmonic Forms, Minimal Surfaces and Norms on Cohomology of Hyperbolic $3$-Manifolds
论文作者
论文摘要
我们限制了$ l^2 $ - $ l^2 $谐波$ 1 $ - 在可定向的折叠双曲线$ 3 $ 3 $ manifold $ m $中，其拓扑复杂性，由瑟斯顿规范衡量，取决于$ m $。它概括了布罗克·杜菲尔德的两个不平等现象。我们还使用最小表面和谐波形式的相互作用研究了封闭和刺痛的情况下不平等的清晰度。我们通过在可定向的封闭和垂直双曲线$ 3 $ manifolds上定义两个功能来统一各种结果，并提出几个问题和猜想。
We bound the $L^2$-norm of an $L^2$ harmonic $1$-form in an orientable cusped hyperbolic $3$-manifold $M$ by its topological complexity, measured by the Thurston norm, up to a constant depending on $M$. It generalizes two inequalities of Brock-Dunfield. We also study the sharpness of the inequalities in the closed and cusped cases, using the interaction of minimal surfaces and harmonic forms. We unify various results by defining two functionals on orientable closed and cusped hyperbolic $3$-manifolds, and formulate several questions and conjectures.
