AI 中文总结
研究离散共形映射和圆模式柯西问题的可积性，通过证明准周期边界条件下离散共形映射初值问题的刘维尔可积性及相关圆模式嵌入像的性质，得出圆模式柯西问题可积的结论。
AI 中文摘要
从正方形晶格到黎曼球面的映射，若每个基本正方形的像为调和四边形，则称为离散共形。我们证明了具有准周期边界条件的离散共形映射的初值问题是刘维尔可积的。还表明施拉姆正交正方形网格圆模式嵌入离散共形映射空间的像为辛叶的实部。由此得到圆模式相应柯西问题的可积性。
英文摘要
A map from a square lattice to the Riemann sphere is called discrete conformal if the image of every elementary square is a harmonic quadrilateral. We prove that the initial value problem for discrete conformal maps with quasi-periodic boundary conditions is Liouville integrable. We also show that the image of the embedding of Schramm's orthogonal square grid circle patterns into the space of discrete conformal maps is the real part of a symplectic leaf. As a consequence, we obtain the integrability of the corresponding Cauchy problem for circle patterns.
Comments40 pages, 16 figures
