This article is concerned with the effect of curvature on laminar flame dynamics. This topic is of fundamental interest and it has practical implications in turbulent combustion. It is shown that highly curved premixed flames may be obtained by operating a standard axisymmetric burner in a specific pulsed mode. Collapsing cylindrical flames are observed by submitting the burner to suitably tuned plane pulsations of the flow velocity. The cylindrical flame pattern collapses in an essentially radial motion. In these circumstances the flame cylinder separates unburned inner gases from the burned outer flow. The temporal evolution of the flame may be monitored using schlieren images while the inner flow velocity is determined from particle image velocimetry (PIV). It is shown that these data yield the stretched laminar burning velocity up to very small radii. Models of the stretched laminar burning velocity as a function of curvature are compared to experimental data and Markstein lengths are deduced. These experiments indicate how laminar flames respond to large curvature values. The data gathered may be used to guide modeling efforts in the area of turbulent combustion.