Evolving convex surfaces to constant width ones

Abstract

Given an [Formula: see text]-dimensional convex surface [Formula: see text] in the Euclidean space [Formula: see text], this initial surface can be deformed into a convex surface with constant width by a new evolution model which preserves the convexity of the evolving surface, provided that the initial principal curvatures satisfy a [Formula: see text]-pinching condition. Some examples of the flow are also constructed via spherical harmonic expansion of the support function.

Whitney-Graustein Homotopy of Locally Convex Curves via a Curvature Flow

“…Remark 2.4. In the previous studies [18,24], the Fourier series expansion is applied to study curvature flows. Under the flow (1.4), both the evolution equation (2.6) and (2.7) are half linear.…”