https://neckpinch.com/authors/hayk-mikayelyan/New arXiv papers by Hayk Mikayelyan, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2202.01441/arxiv:2202.01441Thu, 03 Feb 2022 00:00:00 GMTHayk Mikayelyan — We apply the stabilization technique, developed by T. Zelenyak in 1960s for parabolic equations, on curve shortening flow in R³, and derive several new monotonicity formulas. All of them share one main feature: the dependence of the "energy" term on the angle between the position vector and the plane orthogonal to the tangent vector. The first formula deals with the projection of the curve on the unit sphere, and computes the derivative of its length. The second formula is the generalization of the classical formula of G. Huisken, while the third one is the generalization of the monotonicity formula with logarithmic terms previously derived by the author for plane curves.Curve shortening