Abstract:

In this paper, we derive an estimate on the level surface of the potential function of the complete noncompact gradient steady soliton of extended Ricci flow. We show that the average curvature of the level surface of the potential function grows at most linearly with respect to the distance function under certain conditions. Based on that, we prove that the area of the level surface grows at most linearly and the volume of the sublevel sets grows at most quadratically.

Key words: extended Ricci flow, gradient soliton, volume growth