Energy identities and monotonicity for evolving \(k\)-forms on moving Riemannian spaces

DOI10.1007/s00028-017-0410-6zbMath1394.35224OpenAlexW2766401476MaRDI QIDQ1670258

Ahmad Afuni

Publication date: 5 September 2018

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-017-0410-6

zbMATH Keywords

monotonicityYang-Mills heat flowharmonic map heat flowenergy identitiesevolving manifoldsgeometric heat flows

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Calculus on manifolds; nonlinear operators (58C99)

Related Items

Sobolev embeddings into Orlicz spaces and isocapacitary inequalities ⋮ Isoperimetric inequalities in unbounded convex bodies ⋮ Local energy inequalities for mean curvature flow into evolving ambient spaces ⋮ Local regularity for the harmonic map and Yang-Mills heat flows ⋮ Uniform Lipschitz continuity of the isoperimetric profile of compact surfaces under normalized Ricci flow

Cites Work

• Unnamed Item
• Unnamed Item
• Flow by mean curvature inside a moving ambient space
• Mean curvature flow in a Ricci flow background
• The formation of singularities in the harmonic map heat flow
• Asymptotical behaviour of the Yang-Mills flow and singular Yang-Mills connections
• A local regularity theorem for mean curvature flow
• Estimate of singular set of the evolution problem for harmonic maps
• On the evolution of harmonic maps in higher dimensions
• Existence and partial regularity results for the heat flow for harmonic maps
• Partial differential equations. 4th ed
• Monotonicity formulas for parabolic flows on manifolds
• A matrix Harnack estimate for the heat equation
• Monotonicity formula and small action regularity for Yang-Mills flows in higher dimensions
• Regularity theory for mean curvature flow
• Singularity formation in the Yang-Mills flow
• A special Stoke's theorem for complete Riemannian manifolds
• The Motion of a Surface by Its Mean Curvature. (MN-20)