Accepted Paper

Inserted: 7 aug 2024
Last Updated: 30 dec 2024

Journal: Journal of Convex Analysis
Year: 2024

Abstract:

Given a conical point of a convex surface, a robust notion of generalized unit normal is introduced. Its relationship with the polar to the tangent cone implies the $BV$ regularity of our unit normal. We then show that the area of the geodesically convex hull of its image, called angle defect, describes the energy concentration of the Gauss curvature of smooth surfaces approximating the tangent cone at the conical point.

Keywords: Convex surfaces, Conical points, Unit normal, Angle defect

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• Mucci-Saracco-2024.pdf