Four other people were knifed but survived the attacks.
US man 'kills four people' in New York 28-hour rampage
Police said the suspect had stabbed three people to death, hijacked two cars, run over a pedestrian and attacked several others in the violent spree which covered three New York City boroughs.
The attacks are said to have begun after 0500 local time (1000 GMT) on Friday when Mr Gelman allegedly killed his stepfather, Aleksandr Kuznetsov, in Brooklyn's Sheepshead Bay neighbourhood.
The suspect had had a fight with his mother after she refused to allow him to use her car, a Lexus, and 54-year-old Mr Kuznetsov had intervened, police said.
The attacks began after an argument between the suspect and his mother
Less than six hours later, at about 1030 local time, Mr Gelman went to his ex-girlfriend's home where he killed her 56-year-old mother, Anna Bulchenko.
Yelena Bulchenko, 20, is said to have discovered her mother and called police.
The attacker, who was still in the house, then chased her outside and stabbed her 11 times.
The obvious answer: knife control!
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