论文标题
圆锥形奇点的polyakov公式
Polyakov formulas for conical singularities in two dimensions
论文作者
论文摘要
我们研究了ZETA规范的决定因素及其在存在圆锥形奇异性，边界和角落的情况下的变化。对于具有一个或多个平滑边界组件的孤立圆锥形奇点的表面，我们既展示了一个变异的Polyakov公式，又展示了一个集成的Polyakov公式，用于与Riemannian指标的共形变化，并具有与所有单人构成和边界组件平滑的结合因子。我们证明了表面曲线性多边形结构域的类似结果。然后，我们专门研究有限的圆形扇区和锥体，通过两种独立的方法获得了变异的polyakov公式，以依赖决定剂对开头的依赖性。值得注意的是，这需要在顶点上以对数为单数的共形因子。我们进一步获得了有限圆形扇区和锥体决定因素的明确公式。
We investigate the zeta-regularized determinant and its variation in the presence of conical singularities, boundaries, and corners. For surfaces with isolated conical singularities which may also have one or more smooth boundary components, we demonstrate both a variational Polyakov formula as well as an integrated Polyakov formula for the conformal variation of the Riemannian metric with conformal factors which are smooth up to all singular points and boundary components. We demonstrate the analogous result for curvilinear polygonal domains in surfaces. We then specialize to finite circular sectors and cones and via two independent methods obtain variational Polyakov formulas for the dependence of the determinant on the opening angle. Notably, this requires the conformal factor to be logarithmically singular at the vertex. We further obtain explicit formulas for the determinant for finite circular sectors and cones.
