可允许度量下有限能量辛涡旋的渐近行为献给钱敏教授90华诞

假设(X,ω)是一个具有紧致单连通Lie群G Hamilton作用的紧致光滑辛流形.本文证明只要Riemann面的柱形端口具有一个比标准柱形度量增长速度快的线性度量,那么任何一个有限能量辛涡旋将以指数衰减的速度收敛到辛流形X在正则值辛约化的扭曲分支或非扭曲分支上.本文结果无需假设群G在正则水平集上的作用是自由的.因此,它直接推广了Ziltener在群作用自由的假设下得出的相关结果.本文结果在作者关于量子化Kirwan同态的系列工作中有重要应用.

The asymptotic behavior of finite energy symplectic vortices with admissible metrics

Assume(X,ω)is a compact symplectic manifold with a Hamiltonian action of a compact Lie group G.We prove that at cylinder ends whose metrics grow up at least cylindrically fast,a finite energy symplectic vortex exponentially converges to(un)twisted-sectors of the symplectic reduction at a regular value of the moment map,without assuming the group action on the regular level set is free.It generalizes the corresponding results by Ziltener under the free action assumption.The result of this paper has important applications in the study of quantum Kirwan morphism by the authors.