The spectral theory of generalized Laplacians associated to integrable metrics on compact Riemann surfaces

2013/01/09 by Mounir Hajli, Hajli, Mounir
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.1301.1793

openalex publication_date 2013/01/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We extend the spectral theory of generalized Laplacians to integrable metrics on compact Riemann surfaces. As a consequence, we attach in a direct way, a holomorphic analytic torsion to any integrable metrics. We also provide a different approach to define the holomorphic analytic torsion. We prove that both approaches agree.

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