Energy identity and necklessness for a sequence of Sacks-Uhlenbeck maps to a sphere

DOI10.1016/j.anihpc.2018.04.002zbMath1410.58004OpenAlexW2797651686MaRDI QIDQ1755170

Jiayu Li, Xiang Rong Zhu

Publication date: 8 January 2019

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2018.04.002

zbMATH Keywords

harmonic mapenergy identityharmonic sphereperturbed energy functionalSacks-Uhlenbeck map

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Harmonic maps, etc. (58E20) Variational methods for second-order elliptic equations (35J20)

Related Items (6)

The qualitative behavior for 𝛼-harmonic maps from a surface with boundary into a sphere ⋮ Blowup behavior of harmonic maps with finite index ⋮ Uniqueness of Dirac-harmonic maps from a compact surface with boundary ⋮ A gap theorem for \(\alpha\)-harmonic maps between two-spheres ⋮ Energy identity and necklessness for \(\alpha\)-Dirac-harmonic maps into a sphere ⋮ Asymptotic analysis and qualitative behavior at the free boundary for Sacks-Uhlenbeck \(\alpha \)-harmonic maps

Cites Work

• No neck for approximate harmonic maps to the sphere
• Width and finite extinction time of Ricci flow
• A monotonicity formula for Yang-Mills fields
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• Harmonic and quasi-harmonic spheres. II.
• Compensated compactness and Hardy spaces
• On singularities of the heat flow for harmonic maps from surfaces into spheres
• Energy identity for a class of approximate harmonic maps from surfaces
• Energy identity for the maps from a surface with tension field bounded in \(L^{p}\)
• An existence theorem for surfaces of constant mean curvature
• A weak energy identity and the length of necks for a sequence of Sacks-Uhlenbeck \(\alpha \)-harmonic maps
• SMALL ENERGY COMPACTNESS FOR APPROXIMATE HARMONIC MAPPINGS
• Bubble tree for approximate harmonic maps
• Classical Fourier Analysis
• Energy identity for approximations of harmonic maps from surfaces
• Bubbling of the heat flows for harmonic maps from surfaces
• Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman
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