Gauge Transformation Flow On Riemannian Surfaces And The Neck Analysis Of Polyharmonic Maps

This dissertation consists of two parts.In the first part,we consider the gauge trans-formation of the metric G-bundle on a compact Riemannian surface with boundary.The short-time existence of the flow and the long-time existence of generalized solution are proved.As an application,we derive a heat flow proof for the Uhlenbeck-Riviere de-composition.In the second part,we prove that the energy identity and no neck property hold for a sequence of exterior polyharmonic maps with uniformly bounded energy in the blow-up process.