曲面四角化偏微分方程  

Partial Differential Equations in Surface Quadrangulations

作　　者：刘彦佩[1] 

机构地区：[1]北京交通大学数学研究所,北京100044

出　　处：《昆明理工大学学报（自然科学版）》2012年第5期79-87,94,共10页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：国家自然科学基金(11171020)

摘　　要：本文旨在以球面(或平面,可定向亏格0曲面)为基础,讨论通过数射影面(不可定向亏格1曲面)、环面(可定向亏格1曲面)和Klein瓶(不可定向亏格2曲面)上的四角化所导出的偏微分方程组,建立了这些方程组在一个整域扩张上的定性理论和求解方法.并且,导出了所有这些解使得任何项系数皆正项和的显式.由此启示,一般高亏格曲面的情形,完全可以在球面的基础上,由较小亏格曲面通过一个偏微分方程组所确定.The purpose of this paper is to discuss the partial differential equations arising from counting rooted isomorphic classes of near quadrangulations on the projective plane,torus and Klein bottle with two parameters： the size and the root-face valency by determining the well-definedness on the extension of integral domain.The solution is extracted in form as all coefficients of xm yn as summations of any term positive.These all suggest us to do further for surfaces of genus arbitrarily given via partial differential equations on the basis of certain surfaces of smaller genera from the sphere.

关 键 词：曲面 四角化 整域扩张 偏微分方程 LAURENT级数 

分 类 号：O157[理学—数学]