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Generalized Maximal Diameter Theorems

Year 2024, , 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, , 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

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.