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Generalized Maximal Diameter Theorems

Year 2024, Volume: 17 Issue: 1, 199 - 206, 23.04.2024
https://doi.org/10.36890/iejg.1384669

Abstract

We prove Maximal Diameter Theorems for pointed Riemannian manifolds which are compared to surfaces of revolution with weaker radial attraction.

References

  • [1] Boonnam, N.: A generalized maximal diameter sphere theorem. Tohoku Math. J. 71 145-155 (2019).
  • [2] Gluck H., Singer, D.: Scattering of geodesic fields II. Annals of Math. 110 205-225 (1979).
  • [3] Hebda, J., Ikeda, Y.: Replacing the Lower Curvature Bound in Toponogov’s Comparison Theorem by a Weaker Hypothesis. Tohoku Math. J. 69 305-320 (2017).
  • [4] Hebda, J., Ikeda, Y.: Necessary and Sufficient Conditions for a Triangle Comparison Theorem. Tohoku Math. J. 74 329-364 (2022).
  • [5] Innami, N., K. Shiohama, K., Uneme, Y.: The Alexandrov–Toponogov Comparison Theorem for Radial Curvature. Nihonkai Math. J. 24 57-91 (2013).
  • [6] Itokawa, Y., Machigashira, Y., Shiohama, K.:Generalized Toponogov’s Theorem for manifolds with radial curvature bounded below. Contemporary Mathematics. 332 121-130 (2003).
  • [7] Shiohama, K., and Tanaka, M.: Compactification and maximal diameter theorem for noncompact manifolds with curvature bounded below. Mathematische Zeitschrift. 241 341-351 (2002).
  • [8] Sinclair, R., Tanaka, M.: The cut locus of a sphere of revolution and Toponogov’s comparison theorem. Tohoku Math. J. 59 379-399 (2007).
  • [9] Soga, T.: Remarks on the set of poles on a pointed complete surface. Nihonkai Math. J. 22 23-37 (2011).
  • [10] Tanaka, M.: On a characterization of a surface of revolution with many poles. Mem. Fac. Sci. Kyushu Univ. Ser. A 46 251-268(1992).
Year 2024, Volume: 17 Issue: 1, 199 - 206, 23.04.2024
https://doi.org/10.36890/iejg.1384669

Abstract

References

  • [1] Boonnam, N.: A generalized maximal diameter sphere theorem. Tohoku Math. J. 71 145-155 (2019).
  • [2] Gluck H., Singer, D.: Scattering of geodesic fields II. Annals of Math. 110 205-225 (1979).
  • [3] Hebda, J., Ikeda, Y.: Replacing the Lower Curvature Bound in Toponogov’s Comparison Theorem by a Weaker Hypothesis. Tohoku Math. J. 69 305-320 (2017).
  • [4] Hebda, J., Ikeda, Y.: Necessary and Sufficient Conditions for a Triangle Comparison Theorem. Tohoku Math. J. 74 329-364 (2022).
  • [5] Innami, N., K. Shiohama, K., Uneme, Y.: The Alexandrov–Toponogov Comparison Theorem for Radial Curvature. Nihonkai Math. J. 24 57-91 (2013).
  • [6] Itokawa, Y., Machigashira, Y., Shiohama, K.:Generalized Toponogov’s Theorem for manifolds with radial curvature bounded below. Contemporary Mathematics. 332 121-130 (2003).
  • [7] Shiohama, K., and Tanaka, M.: Compactification and maximal diameter theorem for noncompact manifolds with curvature bounded below. Mathematische Zeitschrift. 241 341-351 (2002).
  • [8] Sinclair, R., Tanaka, M.: The cut locus of a sphere of revolution and Toponogov’s comparison theorem. Tohoku Math. J. 59 379-399 (2007).
  • [9] Soga, T.: Remarks on the set of poles on a pointed complete surface. Nihonkai Math. J. 22 23-37 (2011).
  • [10] Tanaka, M.: On a characterization of a surface of revolution with many poles. Mem. Fac. Sci. Kyushu Univ. Ser. A 46 251-268(1992).
There are 10 citations in total.

Details

Primary Language English
Subjects Algebraic and Differential Geometry
Journal Section Research Article
Authors

James Hebda 0000-0001-5484-1428

Yutaka Ikeda 0000-0001-5430-7102

Early Pub Date April 6, 2024
Publication Date April 23, 2024
Submission Date November 1, 2023
Acceptance Date December 5, 2023
Published in Issue Year 2024 Volume: 17 Issue: 1

Cite

APA Hebda, J., & Ikeda, Y. (2024). Generalized Maximal Diameter Theorems. International Electronic Journal of Geometry, 17(1), 199-206. https://doi.org/10.36890/iejg.1384669
AMA Hebda J, Ikeda Y. Generalized Maximal Diameter Theorems. Int. Electron. J. Geom. April 2024;17(1):199-206. doi:10.36890/iejg.1384669
Chicago Hebda, James, and Yutaka Ikeda. “Generalized Maximal Diameter Theorems”. International Electronic Journal of Geometry 17, no. 1 (April 2024): 199-206. https://doi.org/10.36890/iejg.1384669.
EndNote Hebda J, Ikeda Y (April 1, 2024) Generalized Maximal Diameter Theorems. International Electronic Journal of Geometry 17 1 199–206.
IEEE J. Hebda and Y. Ikeda, “Generalized Maximal Diameter Theorems”, Int. Electron. J. Geom., vol. 17, no. 1, pp. 199–206, 2024, doi: 10.36890/iejg.1384669.
ISNAD Hebda, James - Ikeda, Yutaka. “Generalized Maximal Diameter Theorems”. International Electronic Journal of Geometry 17/1 (April 2024), 199-206. https://doi.org/10.36890/iejg.1384669.
JAMA Hebda J, Ikeda Y. Generalized Maximal Diameter Theorems. Int. Electron. J. Geom. 2024;17:199–206.
MLA Hebda, James and Yutaka Ikeda. “Generalized Maximal Diameter Theorems”. International Electronic Journal of Geometry, vol. 17, no. 1, 2024, pp. 199-06, doi:10.36890/iejg.1384669.
Vancouver Hebda J, Ikeda Y. Generalized Maximal Diameter Theorems. Int. Electron. J. Geom. 2024;17(1):199-206.