Modification of the sector theorem of Kondo-Tanaka

Abstract

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.