New monotonicity formulas for the curve shortening flow in \(\mathbb{R}^3\)

DOI10.1007/s10231-023-01348-5arXiv2202.01441OpenAlexW4379162765MaRDI QIDQ6046856

Hayk Mikayelyan

Publication date: 6 October 2023

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.01441

zbMATH Keywords

curve shortening flowmonotonicity formula

Mathematics Subject Classification ID

Flows related to mean curvature (53E10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the saddle point property of Abresch-Langer curves under the curve shortening flow
• Curve shortening makes convex curves circular
• On the formation of singularities in the curve shortening flow
• Asymptotic behavior for singularities of the mean curvature flow
• Classification of compact ancient solutions to the curve shortening flow
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Singularities of the curve shrinking flow for space curves
• Asymptotic shape of cusp singularities in curve shortening
• Stabilization technique applied to curve shortening flow in the plane
• The zoo of solitons for curve shortening in $\mathbb{R}^n$
• A local monotonicity formula for mean curvature flow

This page was built for publication: New monotonicity formulas for the curve shortening flow in \(\mathbb{R}^3\)