A thin glass substrate, as well as a method and an apparatus are provided. The glass substrate has a glass having first and second main surfaces and elongated elevations on one of the main surfaces. The elevations rise in a normal direction, have a longitudinal extent that is greater than two times a transverse extent, and have a height, on average, that is less than 100 nm, and with a transverse extent of the elevation smaller than 40 mm. The method includes melting a glass, hot forming the glass, and adjusting a viscosity of the glass so that for the viscosity η1 for a first stretch over a first distance of up to 1.5 m downstream of a flow rate control component and y1 indicating a second distance to a location immediately downstream the flow rate control component the equation lg η1(y1)/dPa·s=(lg η01/dPa·s+a1(y1)) applies.