Equidistribution of Expanding Translates of Curves in Homogeneous Spaces with the Action of(SO(n,1))^(k)  

作　　者：Lei YANG 

机构地区：[1]College of Mathematics,Sichuan University,Chengdu 610000,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第1期205-224,共20页数学学报（英文版）

基　　金：Supported by NSFC(Grant No.11801384);the Fundamental Research Funds for the Central Universities(Grant No.YJ201769)。

摘　　要：Let X=G/Γbe a homogeneous space with ambient group G containing the group H=(SO(n,1))^(k)and x∈X be such that Hx is dense in X.Given an analytic curve?:I=[a,b]→H,we will show that ifφsatisfies certain geometric condition,then for a typical diagonal subgroup A={a(t):t∈R}■H the translates{a(t)?(I)x:t>0}of the curve?(I)x will tend to be equidistributed in X as t→+∞.The proof is based on Ratner's theorem and linearization technique.

关 键 词：EQUIDISTRIBUTION homogeneous spaces Ratner's theorem 

分 类 号：O186.11[理学—数学]