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Pythagorean Theorem & Curvature with Lower or Upper Bound

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Abstract

In this paper, the authors give a comparison version of Pythagorean theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).

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References

  1. Alexander, S., Kapovitch, V. and Petrunin, A., Alexandrov Geometry, 2010.

  2. Burago, Y., Gromov, M. L. and Perel’man, G., A.D. Aleksandrov spaces with curvature bounded below, Uspeckhi Mat. Nank, 47(2), 1992, 3–51.

    MathSciNet  MATH  Google Scholar 

  3. Cheeger, J. and Ebin, D., Comparison theorems in Riemannian geometry, American Elsevier Pub. New York, 1975.

    MATH  Google Scholar 

  4. Grove, K. and Markvorsen, S., New extremal problems for the Riemannian recognition program via Alexandrov geometry, J. AMS, 8(1), 1995, 1–28.

    MathSciNet  MATH  Google Scholar 

  5. Li, N. and Rong, X., Bounding geometry of loops in Alexandrov spaces, J. Diff. Geom., 92(1), 2012, 31–54.

    MathSciNet  MATH  Google Scholar 

  6. Plaut, C., Spaces of Wald-Berestovskii curvature bounded below, J. Geom. Anal., 6, 1996, 113–134.

    Article  MathSciNet  Google Scholar 

  7. Wang, Y. S., A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov’s theorem in Alexandrov geometry, arXiv:1809.09818, 2018.

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Authors and Affiliations

  1. School of Mathematical Sciences (and Lab. math. Com. Sys.), Beijing Normal University, Beijing, 100875, China

    Xiaole Su & Yusheng Wang

  2. School of Mathematics Science, Capital Normal University, Beijing, 100037, China

    Hongwei Sun

Authors
  1. Xiaole Su
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  2. Hongwei Sun
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  3. Yusheng Wang
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Corresponding author

Correspondence to Yusheng Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (No. 11971057) and BNSF Z190003.

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Su, X., Sun, H. & Wang, Y. Pythagorean Theorem & Curvature with Lower or Upper Bound. Chin. Ann. Math. Ser. B 43, 95–114 (2022). https://doi.org/10.1007/s11401-022-0307-8

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  • DOI: https://doi.org/10.1007/s11401-022-0307-8

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