矩形上一类全组合偏差极值问题  

A CLASS OF TOTAL COMBINED DISTORTION EXTREMAL PROBLEM BETWEEN RECTANGLES

作　　者：钱香燕 邹庆玲 杨燕[1] 冯小高[1] QIAN Xiangyan;ZOU Qingling;YANG Yan;FENG Xiaogao(College of Mathematics and Information,China West Normal University,Nanchong,Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《井冈山大学学报（自然科学版）》2024年第2期1-6,共6页Journal of Jinggangshan University (Natural Science)

基　　金：国家自然科学基金项目(11701459)。

摘　　要：给出矩形上组合偏差及全组合偏差的新定义,研究了从矩形到矩形上保持端点对应的所有同胚映射在这两类偏差中的极值问题。运用Euler-Lagrange方程、面积长度法和均值不等式证明,并得到这两类极值问题的解为仿射映射,推广了唐茹月在矩形上组合偏差函数极值问题的解是仿射拉伸变换的结果。The new definitions of total combined distortion and combined distortion between rectangles are proposed.The extremal problem of all homomorphic maps between rectangles that keeping vertices respectively in these two types of biases is studied.We use the Euler-Lagrange equation,the area length method and the mean inequality are used to prove and obtain that the affine mapping is the solution of extremal problem,which extends the main results obtained by Tang Ruyue.

关 键 词：组合偏差 全组合偏差 极值问题 仿射映射 面积长度法 

分 类 号：O174.55[理学—数学]