Are you leaving earlier than your rent contract? Your post implies that the rental contract is valid till the 10th of December, but you gave 2 months notice and set the termination date to 27th of November.
If the landlord agreed to the termination date, check your contract again. I do think you have some wiggle room if the landlord accepted a termination date - i.e. terminated your agreement on a certain date. Regardless of what your contract says, it ends on the 27th of November (assuming thats what the landlord agreed) and you don't owe him any money beyond that period.