Anti-self-dual instantons with Lagrangian boundary conditions I : Elliptic theory

Anti-self-dual instantons with Lagrangian boundary conditions II: Bubbling

We study bubbling phenomena of anti-self-dual instantons on $\H^2\times§$, where $§$ is a closed Riemann surface. The restriction of the instanton to each boundary slice $\{z\}\times§$, $z\in\pd\H^2$ is required to lie in a Lagrangian submanifold of the moduli space of flat connections over $§$ that arises from the restrictions to the boundary of flat connections on a handle body. We establish an energy quantization result for sequences of instantons with bounded energy near $\{0\}\times§$: Either their curvature is in fact uniformly bounded in a neighbourhood of that slice (leading to a compa…

Yang-Mills方程在瞬子-反瞬子配置附近的行为

The Yang-Mills equation near instanton-anti-instanton configurations

研究非瞬子Yang-Mills连接序列是否能趋近于仅由瞬子组成的气泡配置，证明瞬子是能量小于特定值的SU(2)Yang-Mills方程在R^4上的唯一解，并证明能量谱的离散性。

Harmonic functions and instanton moduli spaces on the multi-Taub--NUT space

Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with respect to the trivial flat connection and decay rapidly. The resulting unital energy anti-instantons have trivial holonomy at infinity. We also fully describe their unframed moduli space and find that it is a five dimensional space admitting a singular disk-fibration over R^3. On the way, we work out in detail the twistor space of the multi-Taub--NUT geometry t…