The first gap for total curvatures of planar graphs with nonnegative curvature. Issue 3 (30th September 2019) - Hua, Bobo; Su, Yanhui
Abstract: We prove that the total curvature of a planar graph with nonnegative combinatorial curvature is at least 1/12 if it is positive. Moreover, we classify the metric structures of ambient polygonal surfaces for planar graphs attaining this bound.