关于保持距离映射的aleksandrov问题

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1、(4)LetXandYbetwoquasiconvex2-normedlinearspaces.SupposethatfXYbeaffineanditpreserveallareasm<1.Thenfisan2-isometry.Thesecondsection,isdevotedtotheAleksandrovprobleminHibertspace,themainresults：(1)LetXandYbeHibertspaces,dimX>2,assumethatf：XYpreservestwodistance

2、s1and^n2-1+^m2-1,thenfisalinearisometryuptotranslation.(2)LetXandYbeHibertspaces,dimX>2,assumethatf：XYpreservestwodistances1andy^.n2-§+^Jm2-1,thenfisalinearisometryuptotranslation.Inthethirdsection,weconsideredtheAleksandrovprobleminRnspace.weprovedthat：Assume

3、thatf：Rn-1——^Rnpreservestwodistances1andU/k2-x2a_2+ym2-ᕷ_2)，thenfisalinearisometryuptotranslation.(x2_^^n==-21(_1)i(n_i)2)(xn_2_(n_1)2).KeyWords:isometry;Aleksandrovproblem;quasi-convexnormedlinearspace;Hilbertspace;Rnspace.万方数据!îoí"#..........................

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