Sharp glass edges become smooth on heating it to its melting point in a flame because upon heating, the glass melts and the surface of the liquid tends to take the spherical shape at the edges which has minimum surface area, and edges rounded up and become smooth. This is called fire polishing of glass. It is used to make sharp edges smooth.
The property of liquid which is responsible for this phenomenon is known as “Surface tension” of the liquid due to which the melted glass tends to take the minimum surface area.