TY - JOUR T1 - Generalized Maximal Diameter Theorems AU - Hebda, James AU - Ikeda, Yutaka PY - 2024 DA - April Y2 - 2023 DO - 10.36890/iejg.1384669 JF - International Electronic Journal of Geometry JO - Int. Electron. J. Geom. PB - Kazım İlarslan WT - DergiPark SN - 1307-5624 SP - 199 EP - 206 VL - 17 IS - 1 LA - en AB - We prove Maximal Diameter Theorems for pointed Riemannian manifolds which are compared to surfaces of revolution with weaker radial attraction. KW - Maximal diameter theorem KW - maximal perimeter theorem KW - weaker radial attraction CR - [1] Boonnam, N.: A generalized maximal diameter sphere theorem. Tohoku Math. J. 71 145-155 (2019). CR - [2] Gluck H., Singer, D.: Scattering of geodesic fields II. Annals of Math. 110 205-225 (1979). CR - [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). CR - [4] Hebda, J., Ikeda, Y.: Necessary and Sufficient Conditions for a Triangle Comparison Theorem. Tohoku Math. J. 74 329-364 (2022). CR - [5] Innami, N., K. Shiohama, K., Uneme, Y.: The Alexandrov–Toponogov Comparison Theorem for Radial Curvature. Nihonkai Math. J. 24 57-91 (2013). CR - [6] Itokawa, Y., Machigashira, Y., Shiohama, K.:Generalized Toponogov’s Theorem for manifolds with radial curvature bounded below. Contemporary Mathematics. 332 121-130 (2003). CR - [7] Shiohama, K., and Tanaka, M.: Compactification and maximal diameter theorem for noncompact manifolds with curvature bounded below. Mathematische Zeitschrift. 241 341-351 (2002). CR - [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). CR - [9] Soga, T.: Remarks on the set of poles on a pointed complete surface. Nihonkai Math. J. 22 23-37 (2011). CR - [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). UR - https://doi.org/10.36890/iejg.1384669 L1 - https://dergipark.org.tr/en/download/article-file/3510821 ER -