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- W4361761386 abstract "Abstract For any real number <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>κ</m:mi> </m:math> kappa and any integer <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>n</m:mi> <m:mo>≥</m:mo> <m:mn>4</m:mn> </m:math> nge 4 , the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mi mathvariant=normal>Cycl</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {{rm{Cycl}}}_{n}left(kappa ) condition introduced by Gromov ( CAT(κ)-spaces: construction and concentration , Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 280 (2001), (Geom. i Topol. 7), 100–140, 299–300) is a necessary condition for a metric space to admit an isometric embedding into a <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=normal>CAT</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {rm{CAT}}left(kappa ) space. For geodesic metric spaces, satisfying the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mi mathvariant=normal>Cycl</m:mi> </m:mrow> <m:mrow> <m:mn>4</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {{rm{Cycl}}}_{4}left(kappa ) condition is equivalent to being <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=normal>CAT</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {rm{CAT}}left(kappa ) . In this article, we prove an analogue of Reshetnyak’s majorization theorem for (possibly non-geodesic) metric spaces that satisfy the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mi mathvariant=normal>Cycl</m:mi> </m:mrow> <m:mrow> <m:mn>4</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {{rm{Cycl}}}_{4}left(kappa ) condition. It follows from our result that for general metric spaces, the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mi mathvariant=normal>Cycl</m:mi> </m:mrow> <m:mrow> <m:mn>4</m:mn> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {{rm{Cycl}}}_{4}left(kappa ) condition implies the <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mrow> <m:mi mathvariant=normal>Cycl</m:mi> </m:mrow> <m:mrow> <m:mi>n</m:mi> </m:mrow> </m:msub> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>κ</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {{rm{Cycl}}}_{n}left(kappa ) conditions for all integers <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi>n</m:mi> <m:mo>≥</m:mo> <m:mn>5</m:mn> </m:math> nge 5 ." @default.
- W4361761386 created "2023-04-04" @default.
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- W4361761386 date "2023-01-01" @default.
- W4361761386 modified "2023-09-25" @default.
- W4361761386 title "A non-geodesic analogue of Reshetnyak’s majorization theorem" @default.
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- W4361761386 doi "https://doi.org/10.1515/agms-2022-0151" @default.
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