The isoperimetric quotient of a convex body decreases monotonically under the Eikonal abrasion model

Abstract

We show that under the Eikonal abrasion model, prescribing uniform normal speed in the direction of the inward surface normal, the isoperimetric quotient of a convex shape is decreasing monotonically.

The proof of Theorem 1 holds only under additional assumptions. For more details, see arXiv:1910.05367

References in corpus (3)

• Formation of sharp edges and planar areas of asteroids by polyhedral abrasion
• Explaining the elongated shape of 'Oumuamua by the Eikonal abrasion model
• A bound for the perimeter of inner parallel bodies