1) By ITU Standards(IMT-A) are there any live 4G networks ?  Also what are the mandatory requirements for these technologies.
2) By ITU standards, what the definition of an Heterogeneous Network wrt IMT-A
3) Is there a study group within the ITU that seeks to standardize Mobility Management across heterogeneous network.

Thank you very much for your question. Since the answer to the first two of your questions is in the ITU-R area the answer was coordinated with our colleagues from BR who invited you to take a look at the dedicated webpage:
http://www.itu.int/ITU-R/index.asp?...mp;lang=en to find IMT-Advanced information within ITU-R SG5.  The requirements are indicated in Recommendation ITU-R M.1645 "Framework and overall objectives of the future development of IMT-2000 and systems beyond IMT-2000"
http://www.itu.int/rec/R-REC-M.1645/en.

To answer your last question we are glad to let you know that yes, we do have such a group. It is ITU-T SG 13 and Question 22/13 “Mobility Management and Fixed Mobile Convergence” in particular. This Question will meet in Geneva from 10 to 21 October 2011. The group has already approved some Recommendation covering different aspects of mobility management. Please look in the Y.2800-series http://www.itu.int/rec/T-REC-Y/e.