This article investigates the mobility management of an ultra dense cellular network (UDN) from an energy-efficiency (EE) point of view. Many dormant base stations (BSs) in a UDN do not transmit signals, and thus a received power based handover (HO) approach as in traditional cellular networks is hardly applicable. In addition, the limited front/backhaul capacity compared to a huge number of BSs makes it difficult to implement a centralized HO and power control. For these reasons, a novel user-centric association rule is proposed, which jointly optimizes HO and power control for maximizing EE. The proposed mobility management is able to cope not only with the spatial randomness of user movement but also with temporally correlated wireless channels. The proposed approach is implemented over a HO time window and tractable power control policy by exploiting mean-field game (MFG) and stochastic geometry (SG). Compared to a baseline with a fixed HO interval and transmit power, the proposed approach achieves the 1.2 times higher long-term average EE at a typical active BS.