Mapping of Least ρ-Dirichlet Energy between Doubly Connected Riemann Surfaces  

作　　者：Li ZHANG Sheng Jin HUO Hui GUO Xiao Gao FENG 

机构地区：[1]College of Mathematics and Information,China West Normal University,Nanchong 637002,P.R.China [2]Department of Mathematics,Tianjin Polytechnic University,Tianjin 300387,P.R.China [3]College of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2020年第6期663-672,共10页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11701459);the Natural Science Foundation of Sichuan Provincial Department of Education(Grant No.17ZB0431);the Research Startup of China West Normal University(Grant No.17E88);supported by the Science and Technology Development Fund of Tianjin Commission for Higher Education(Grant No.2017KJ095)。

摘　　要：In this note,we consider the mappings h:X→Y between doubly connected Riemann surfaces having leastρ-Dirichlet energy.For a pair of doubly connected Riemann surfaces,in which X has finite conformal modulus,we establish the following principle:A mapping h in the class H2(X,Y)of strong limits of homeomorphisms in Sobolev space W1,2(X,Y)isρ-energy-minimal if and only if its Hopf-differential is analytic in X and real along?X.It improves and extends the result of Iwaniec et al.(see Theorem 1.4 in[Arch.Ration.Mech.Anal.,209,401–453(2013)]).Furthermore,we give an application of the principle.Anyρ-energy minimal diffeomorphism isρ-harmonic,however,we give a 1/|w|~2-harmonic diffemorphism which is not 1/|w|~2-energy minimal diffeomorphism.At last,we investigate the necessary and sufficient conditions for the existence of 1/|w|~2-harmonic mapping from doubly connected domainΩto the circular annulus A(1,R).

关 键 词：ρ-Dirichlet energy Hopf-differential ρ-harmonic mapping ρ-Nitsche conjecture 

分 类 号：O186.12[理学—数学]