Study on periodic surfaces using their representations by integrals of conformal one-forms

欧几里得（四）空间中最小曲面的Lopez-Ros变形与与最小曲面相关的两个平面连接族的修整变换之间的对应关系被Katrin Leschke博士的共同工作所清除。这一结果曾在国内外会议和研讨会上发表。研究了调和平均曲率逆及其变换的推广。该研究结果发表在一份国际期刊上。得到了四维欧几里德空间中超共形曲面的Schwarz引理的一个类比。关于这一结果的预印本已经写好并提交给了一家国际期刊。推广了全纯一型的Riemann双线性关系，得到了周期曲面存在的一个条件。关于这一结果的预印本已经写好并提交给了一家国际期刊。

The correspondence between the Lopez-Ros deformation of a minimal surface in Euclidean (four-)space and the dressing transformations of two families of flat connections associated with a minimal surface was cleared by the joint work with Dr, Katrin Leschke.This result was presented in domestic or foreign conferences and seminars. A generalization of harmonic inverse mean curvature and their transforms was studied. The result was published in an international journal. An analog of the Schwarz lemma for super-conformal surfaces in four-dimenaional Euclidean space is obtained. A preprint about this result was written and submitted to an international journal. Generalizing the Riemann bilinear relation for holomorhphic one-forms, a condition for the existence of periodic surfaces was obtained. A preprint about this result was written and submitted to an international journal.