The aim of this paper is to determine the structure of the cut locus for a class of surfaces of revolution homeomorphic to a cylinder. Let $M$ denote a cylinder of revolution which admits a reflective symmetry fixing a parallel called the equator of $M$. It will be proved that the cut locus of a point $p$ of $M$ is a subset of the union of the meridian and the parallel opposite to $p$ respectively, if the Gaussian curvature of $M$ is decreasing on each upper half meridian.
"The Structure Theorem for the Cut Locus of a Certain Class of Cylinders of Revolution I." Tokyo J. Math. 37 (2) 473 - 484, December 2014. https://doi.org/10.3836/tjm/1422452803