Harmonic Maps with Free Boundary from Degenerating Bordered Riemann Surfaces

被引：0
作者：
Lei Liu
Chong Song
Miaomiao Zhu
机构：
[1] Central China Normal University,School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences
[2] Xiamen University,School of Mathematical Sciences
[3] Shanghai Jiao Tong University,School of Mathematical Sciences, IMA
来源：
The Journal of Geometric Analysis | 2022年 / 32卷
关键词：
Harmonic map; Degenerating bordered Riemann surface; Free boundary; Blow-up; 58E15; 35J50; 35R35;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the blow-up analysis and qualitative behavior for a sequence of harmonic maps with free boundary from degenerating bordered Riemann surfaces with uniformly bounded energy. With the help of Pohozaev type constants associated to harmonic maps defined on degenerating collars, including vertical boundary collars and horizontal boundary collars, we establish a generalized energy identity.
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[1]  
Chen L(2012)The refined analysis on the convergence behavior of harmonic map sequence from cylinders J. Geom. Anal. 22 942-963
[2]  
Li Y(1969)The irreducibility of the space of curves of given genus Inst. Hautes Études Sci. Publ. Math. 36 75-109
[3]  
Wang Y(1995)Energy identity for a class of approximate harmonic maps from surfaces Commun. Anal. Geom. 3 543-554
[4]  
Deligne P(1985)Pseudo holomorphic curves in symplectic manifolds Invent. Math. 82 307-347
[5]  
Mumford D(1987)Harmonic maps which solve a free-boundary problem J. Reine Angew. Math. 381 61-89
[6]  
Ding W(2019)Vanishing Pohozaev constant and removability of singularities J. Differ. Geom. 111 91-144
[7]  
Tian G(2019)The qualitative behavior at the free boundary for approximate harmonic maps from surfaces Math. Ann. 374 133-177
[8]  
Gromov M(2020)Energy quantization for a singular super-Liouville boundary value problem Math. Ann. 381 905-969
[9]  
Gulliver R(2001)Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc Adv. Theor. Math. Phys. 5 1-49
[10]  
Jost J(2017)Regularity and quantification for harmonic maps with free boundary Adv. Calc. Var. 10 69-82
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