Correction to: A Polyakov Formula for Sectors

Other text in scientific journal, 2020

Let 𝑆𝛼 denote a finite circular sector of opening angle 𝛼∈(0,𝜋) and radius one, and let 𝑒−𝑡Δ𝛼 denote the heat operator associated to the Dirichlet extension of the Laplacian. Based on recent joint work [2] and [3], we discovered an extra contribution to the variational Polyakov formula in [1] coming from the curved boundary component of the sector. Theorems 3 and 4 of [1] should have an added term +14𝜋. This calculation will appear in [2]. The corrected statements of these theorems are given below.