Kondo-Tanaka proved that if a rotationally symmetric plane $M_m$ is von Mangoldt or Cartan-Hadamard outside a compact set and has finite total curvature, then it has a sector with no pair of cut points. We show that the condition of finite total curvature can be removed. %The abstract should provide clear information about the research and the results obtained, and should not exceed 200 words. The abstract should not contain citations.
Radial curvature, critical point, surface of revolution, finite topological type, finite total curvature, cut point, conjugate point
"Modification of the sector theorem of Kondo-Tanaka,"
Turkish Journal of Mathematics: Vol. 47:
6, Article 13.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss6/13