Lowner微分方程与调和拟共形映射  

Lowner Different Equation and Harmonic Quasiconformal Mapping

作　　者：聂云梦 黄华鹰[1] NIE Yunmeng;HUANG Huaying(School of Mathematical Sciences,Anhui University,230601,Hefei,Anhui,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《淮北师范大学学报（自然科学版）》2020年第4期1-6,共6页Journal of Huaibei Normal University：Natural Sciences

基　　金：安徽省自然科学基金面上项目(1908085MA18)。

摘　　要：文章研究Lowner微分方程dw dt=F(w,t)中F(ω,t)与方程解ω=f(z,t)之间的关系问题.利用F(ω,t)的可微性,得到具有调和同胚解的Lowner微分方程所需的必要条件,并证明当方程存在形如ω=f(z,t)=u(x,y,t)+iy的K(t)-调和拟共形映射解时,F(ω,t)是调和映射.特别地,若u(z,t)∈C2(H,[0,T]),则F(ω,t)是调和拟共形形变.This paper studies the relationship between F(ω,t)and equation solutionsω=f(z,t)in the Lown⁃er differention equation.Using the differentiability of F(ω,t),the necessary conditions for the Lowner differen⁃tial equation with the solution of the harmonic homeomorphism are obtained,and proves that the function F(ω,t)is harmonic when the equation has a the solution of the K(t)-harmonic quasiconformal mapping of the formω=f(z,t)=u(x,y,t)+iy.In particular,if u(z,t)∈C2(H,[0,T]),then F(ω,t)is harmonic quasiconfor⁃mal deformation.

关 键 词：调和同胚 调和拟共形映射 Lowner微分方程 调和拟共形形变 

分 类 号：O174.5[理学—数学]