How did the soviet union maintain control of east germany after world war ii?

I believe the answer is: The soviets kept their troops in east Germany and occupied it

The existence of soviet union troops allow them to influence east germany's political extend. This lead to a situation when there were two opposite ideologies exist in germany.  The eastern Germany that controlled by soviet union adopted a communism ideology while the western Germany that controlled by the Allies adopted a democratic ideology.

what are local authorities doing to fix the problem

explanation:

what are local authorities doing to fix the problem

ok, but what is your question? as soon as you tell me i will answer your question : )