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

  • Robert S. StrichartzEmail author
Article
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Abstract

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

53A05 

Notes

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Mathematics DepartmentCornell UniversityIthacaUSA

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