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

欧几里德(四维)空间中极小曲面的Lopez-Ros变形与与极小曲面相关的两族平面连通族的Dressing变换之间的对应关系已被Katrin Leschke博士证明.这一结果已在国内外的会议和研讨会上公布.研究了调和逆平均曲率及其变换的一个推广。这项研究结果发表在一份国际期刊上。得到了四维欧氏空间中超共形曲面的Schwarz引理的一个类似结果。关于这一结果的预印本被撰写并提交给一家国际期刊。将Riemann双线性关系推广到全纯单形，得到了周期曲面存在的一个条件。关于这一结果的预印本被撰写并提交给一家国际期刊。

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.