Energy identity for approximations of harmonic maps from surfaces

2007/05/31 by Lamm, Tobias · 3 citations
#35J60 #53C43 #58E20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0705.4589

Abstract

We prove the energy identity for min-max sequences of the Sacks-Uhlenbeck and the biharmonic approximation of harmonic maps from surfaces into general target manifolds. The proof relies on Hopf-differential type estimates for the two approximations and on estimates for the concentration radius of bubbles.

Cited by

• The quantitative behavior of α-Yang-Mills-Higgs fields on surfaces
• Higher dimensional Sacks-Uhlenbeck-type functionals and applications
• Stability of the Morse Index for the p-harmonic Approximation of Harmonic Maps into Homogeneous Spaces

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