论文标题
伪laplacian在尖端的统一统一线束上
Pseudo-Laplacian on a cuspidal end with a flat unitary line bundle: Alvarez--Wentworth boundary conditions
论文作者
论文摘要
cuspidal端是一种公制奇异性，被描述为$ s^1 \ times \ left] a， +\ infty \ right [$ withpoincaréMetric。基础集也可以看作是$ \ mathbb {r} \ times \ left] a， +\ infty \ right [$受翻译$ t的动作$ t：\ left（x，x，y \ right）\ longirins \ longirins arrow \ left（x +1，y \ right）$。在上面，人们可能会考虑一个全态线束$ l $，来自$ t $产生的集团的统一特征。复杂的模量在$ L $上诱导平坦的度量标准，并且伪拉普拉斯$δ__{l，0} $作用于函数，可能与Chern Connection相关联。一个人需要指定边界条件，在这里它们被选为Alvarez-Wentworth边界条件，这是Dirichlet和Neumann边界条件的组合。本文的目的是找到Zeta调控的$ \ det \ left的渐近行为（Δ_{l，0} +μ\ right）$，为$μ> 0 $ to in Infinity for noith $ a $，也可以作为$ a $ a $ for infinity for $μ= 0 $ = 0 $。
A cuspidal end is a type of metric singularity, described as a product $S^1 \times \left] a, +\infty \right[$ with the Poincaré metric. The underlying set can also be seen as $\mathbb{R} \times \left] a, +\infty \right[$ subject to the action of the translation $T : \left( x,y \right) \longrightarrow \left( x+1, y \right)$. On it, one may consider a holomorphic line bundle $L$, coming from a unitary character of the group generated by $T$. The complex modulus induces a flat metric on $L$, and a pseudo-Laplacian $Δ_{L,0}$ acting on functions can be associated to the Chern connection. One needs to specify boundary conditions, and they are here chosen to be the Alvarez--Wentworth boundary conditions, which are a combination of Dirichlet and Neumann boundary conditions. The aim of this paper is to find the asymptotic behavior of the zeta-regularized determinant $\det \left( Δ_{L,0} + μ\right)$, as $μ> 0$ goes to infinity for any $a$, and also as $a$ goes to infinity for $μ= 0$.
