The effects of strain rate and curvature on the edge flame propagation characteristics in an igniting turbulent coflowing planar jet are studied based on 3-dimensional compressible Direct Numerical Simulation (DNS) with a modified single-step Arrhenius chemistry. In the present configuration the high-speed jet fluid is considered to be fuel-rich, whereas the slow-moving coflowing fluid is taken to be fuel-lean. Consistent with previous work with DNS without mean flow and shear, the resulting flame from localized forced ignition at the jet exhibits predominantly premixed edge flame structure where premixed flames are formed on both the fuel-rich and fuel-lean sides and the intersection between these two branches propagate on the stoichiometric mixture fraction isosurface. The edge flame propagation behavior has been studied in terms of the statistics of the edge flame displacement speed Sd, which refers to the speed at which the fuel mass fraction YF isosurface moves normal to itself, relative to an initially coincident material surface at the intersection between the fuel-rich and fuel-lean premixed flames on the stoichiometric mixture fraction isosurface. The probability density function of the density-weighted edge flame displacement speed S*(d) shows nonzero probability of finding negative values of S*(d) at later stages of self-sustained flame propagation. The mean value of S*(d) decreases after the energy deposition is switched off but eventually settles to a value that does not change appreciably with time. The S*(d) is found to be predominantly negatively correlated with curvature but the correlation between S*(d) and tangential strain rate shows both positive and negative correlating trends with the positive correlating trend dominant at later stages of flame propagation. It has been found that strain rate and curvature dependences of broken vertical bar YF broken vertical bar have significant influences on the statistical behavior of S*d in response to strain rate and curvature. The observed strain rate and curvature dependences of S*(d) have been explained in detail in terms of statistical behaviors of the reaction, normal diffusion, and the tangential diffusion components of S*(d) (i.e., S*(r), S*(n), and S*(t)).