Defining Curvature as a Measure via Gauss–Bonnet on Certain Singular Surfaces

  • Robert S. StrichartzEmail author


We show how to define curvature as a measure using the Gauss–Bonnet Theorem on a family of singular surfaces obtained by gluing together smooth surfaces along boundary curves. We find an explicit formula for the curvature measure as a sum of three types of measures: absolutely continuous measures, measures supported on singular curves, and discrete measures supported on singular points. We discuss the spectral asymptotics of the Laplacian on these surfaces.

Mathematics Subject Classification




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© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentCornell UniversityIthacaUSA

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