Wash the lime in hot water and grate dry. Finely grate the peel. Squeeze the lime. Mix mascarpone and yoghurt briefly with 2-3 tbsp. sugar, vanilla sugar, lime zest and juice. Whip cream until stiff and fold into the mascarpone cream.
Wash, halve and stone the apricots. Drain the apricots from the tin. Puree the fruit in a tall mixing bowl with a hand blender. Sweeten the puree of fresh apricots with 2 tbsp. sugar if necessary.
Spread the mascarpone cream and puree in layers in six glasses. Swirl lightly with a teaspoon of cream and puree. Keep cool until serving.
To serve, place ice cubes in a large bowl or similar. Place glasses with apricot-mascarpone cream in it.