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math.DG2024
The Brioschi Formula for the Gaussian Curvature
Lee-Peng Teo
The Brioschi formula expresses the Gaussian curvature in terms of the functions and in local coordinates of a surface . This implies the Gauss' theorema egregium,…
math.DG2024
Local Index Theorem for Cofinite Hyperbolic Riemann Surfaces
Lee-Peng Teo
We discuss the local index theorem for cofinite Riemann surfaces in a pedagogical way, from a more computational perspective. Given a cofinite Riemann surface , let be the…