Pythagorean Theorem & Curvature with Lower or Upper Bound

Xiaole Su; Hongwei Sun; Yusheng Wang

doi:10.1007/s11401-022-0307-8

Chinese Annals of Mathematics, Series B ›› 2022, Vol. 43 ›› Issue (1) : 95 -114. DOI: 10.1007/s11401-022-0307-8

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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).

Keywords

Pythagorean theorem / Alexandrov space / Toponogov’s theorem

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Xiaole Su, Hongwei Sun, Yusheng Wang. Pythagorean Theorem & Curvature with Lower or Upper Bound. Chinese Annals of Mathematics, Series B, 2022, 43(1): 95-114 DOI:10.1007/s11401-022-0307-8

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References

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

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

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

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

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

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

[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.