The manner of supplying their demand is your wisdom. If you suppress it, it will create further trouble. You have to fulfil it, but how you fulfil it is the wisdom of the seeker. Sometimes you may supply its need even by not giving it literally what it wants. If you literally start supplying all its demands, then it will be a very difficult problem.
Sublimation is different from fulfilment.
Fulfilment is a direct sensual process, whereas sublimation is a spiritual integration. The mind wants some particular things, not all things at the same time. The mind does not want the whole world to be given to it. This is the sign of lack of wisdom behind any kind of desire. There are simple desires, strong desires, permissible desires, depleting desires.