Wash limes hot, dry, thinly grate peel, squeeze juice. Put in a saucepan with the water and sugar and simmer on low heat for 5 min. All together cool down.
Peel the mango, cut the pulp from the core into small wedges and blend with the sugar water in a hand mixer.
Fill the mango puree into a metal bowl and freeze for 3 to 4 hours. Stir with a whisk more often during this time.
Fill the mango sorbet into chilled glasses and serve on the spot.