Boundary bubbling analysis of approximate harmonic maps under either weak or strong anchoring conditions in dimension two

2016/07/19 by Tao Huang, Huang, Tao, Changyou Wang +1
Mathematics · #35E #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.AP #msc:35E

paper · pdf · doi:10.48550/arxiv.1607.05357

32 pages

arxiv created 2016/07/19 · openalex publication_date 2016/07/19 · arxiv updated 2016/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will study the bubbling phenomena of approximate harmonic maps in dimension two that have either (i) bounded L²-tension fields under the weak anchoring condition, or (ii) bounded Llog L ∩ M^1,δ-tension fields under the strong anchoring condition.

Citations

• Introduction to Q-tensor theory
• Energy identity for approximate harmonic maps from surface to general targets

Related

• Remarks on approximate harmonic maps in dimension two
• Analysis of boundary bubbles for almost minimal cylinders
• Removable singularities and bubbling of harmonic maps and biharmonic maps
• Convergence of almost harmonic maps to geodesic bubble trees
• Harmonic Maps of Surfaces Approaching the Boundary of Moduli Space and Eliminating Bubbling