论文标题
重态的能量和可重新提示的奇异谐波图中的平面域上的紧凑型歧管
Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains
论文作者
论文摘要
我们为地图定义了重量化的能量，这些图描述了由于边界数据产生的障碍物和目标歧管的mutliple连接性而产生的奇异性之外的谐波图的一阶渐近学。该结构概括了伯特埃尔，布雷兹斯和赫莱因圆圈的定义（Ginzburg-Landau Vortices，1994年）。通常，奇异性是几何物体，可以通过新的同性恋概念来研究对同位奇异性的依赖。重构的能量显示为强制性和利润率连续。重量化的能量与最大程度地减少可重新符号的奇异谐波图有关，并且可以最大程度地减少点的构型，可以通过奇异性的应力 - 能量张量的通量来表征。我们在几种特殊情况下计算奇异能量和重量化的能量。
We define renormalised energies for maps that describe the first-order asymptotics of harmonic maps outside of singularities arising due to obstructions generated by the boundary data and the mutliple connectedness of the target manifold. The constructions generalise the definition by Bethuel, Brezis and Hélein for the circle (Ginzburg-Landau vortices, 1994). In general, the singularities are geometrical objects and the dependence on homotopic singularities can be studied through a new notion of synharmony. The renormalised energies are showed to be coercive and Lipschitz-continuous. The renormalised energies are associated to minimising renormalisable singular harmonic maps and minimising configurations of points can be characterised by the flux of the stress-energy tensor at the singularities. We compute the singular energy and the renormalised energy in several particular cases.
