He has widely published and presented his research in the area of hyperbolic manifolds and ending lamination spaces. His most notable work is the proof of existence of Cannon–Thurston maps.[9][10] This led to the resolution of the conjecture that connected limit sets of finitely generated Kleinian groups are locally connected.[4] He is also the author of a book titled Maps on boundaries of hyperbolic metric spaces.[11]
Mj became a monk of the Ramakrishna order in 1998.[5] Mahan Maharaj, as he is known to his students and colleagues, is fluent in English, Hindi and Bengali. He also knows a bit of Tamil, learnt from his stay in southern part of India at IMSc. He has been quoted as saying, "I am enjoying being a monk as much as I enjoy my mathematics".[12]