Mobility has become a basic premise of network communications, thereby requiring a native integration into 5G networks. Despite the numerous efforts to propose and to standardize effective mobility management models for IP, the result is a complex, poorly flexible set of mechanisms. The natural support for mobility offered by ICN (Information Centric Networking), makes it a good candidate to define a radically new solution relieving limitations of traditional approaches. If consumer mobility is supported in ICN by design, in virtue of its connectionless pull-based communication model, producer mobility is still an open challenge. In this work, we propose MAP-Me, an anchor-less solution to manage micro mobility of content producer via ICN name-based data plane, with support for latency-sensitive applications. First, we analyze MAP-Me performance and provide guarantees of correctness and stability. Further, we set up a realistic simulation environment in NDNSim 2.1 for MAP-Me evaluation and comparison against existing solutions: either random waypoint and trace-driven car mobility patterns are considered under 802.11 radio access. Results are encouraging and highlight the superiority of MAP-Me in terms of user performance and of network cost metrics.