A local monotonicity formula for mean curvature flow

DOI10.2307/3062105zbMath1007.53050OpenAlexW2007140928MaRDI QIDQ5953609

Klaus Ecker

Publication date: 16 March 2003

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3062105

zbMATH Keywords

mean curvature flowheat equation solution estimate

Mathematics Subject Classification ID

Calculus on manifolds; nonlinear operators (58C99) Isospectrality (58J53) Equations in function spaces; evolution equations (58D25)

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Bounding dimension of ambient space by density for mean curvature flow ⋮ Mean Curvature Flow in Higher Codimension: Introduction and Survey ⋮ New monotonicity formulae for semi-linear elliptic and parabolic systems ⋮ New monotonicity formulas for the curve shortening flow in \(\mathbb{R}^3\) ⋮ A local Sobolev inequality on Ricci flow and its applications ⋮ A sharp bound for the area of minimal surfaces in the unit ball ⋮ Mean curvature flow with free boundary outside a hypersphere ⋮ Local monotonicity and mean value formulas for evolving Riemannian manifolds ⋮ Local energy inequalities for mean curvature flow into evolving ambient spaces ⋮ Heat ball formulæ for \(k\)-forms on evolving manifolds ⋮ On the entropy of parabolic Allen-Cahn equation ⋮ On Ecker's local integral quantity at infinity for ancient mean curvature flows ⋮ Local monotonicity formulas for some nonlinear diffusion equations ⋮ Minimal cones and self-expanding solutions for mean curvature flows ⋮ Mean curvature flow ⋮ Local monotonicity for the Yang-Mills-Higgs flow

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