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

作     者：Lei YANG Lei YANG

作者机构：College of MathematicsSichuan UniversityChengdu 610000P.R.China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2022年第38卷第1期

页      面：205-224页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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

主　　题：Equidistribution homogeneous spaces Ratner's theorem 

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 *** 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:t0}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.