Geometric Analysis on non-compact spaces and the geometry of infinite dimensional moduli spaces

我专注于最重要的结果。构造了一个没有非平凡实例的有向完全黎曼4流形的例子。研究了曲率在三球与直线积空间上一致有界的ASD连接的模空间。我们得到了它们的局部平均维数与连接的能量密度之间的估计。我们得到了Brody曲线空间的平均维数与曲线能量密度之间的一个估计。特别地，我们得到了一个精确的公式用能量密度来表示平均维数在目标空间是黎曼球的情况下。

I concentrate on the most important results. I constructed an example of oriented complete Riemannian 4-manifolds having no non-trivial instanton. We studied moduli spaces of ASD connections whose curvatures are uniformly bounded over the product space of 3-sphere and the line. We got an estimate relating their local mean dimension to the energy densities of connections. We got an estimate relating a mean dimension of the space of Brody curves to the energy densities of curves. In particular we got an exact formula which represents the mean dimension by using the energy densities in the case that the target space is the Riemann sphere.