The geometry of fronts

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Abstract

We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges. Moreover, it is closely related to the behavior of the Gaussian curvature of a surface near cuspidal edges and swallowtails.

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Saji, K., Umehara, M., & Yamada, K. (2009). The geometry of fronts. Annals of Mathematics, 169(2), 491–529. https://doi.org/10.4007/annals.2009.169.491

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