I think I figured it out ;) 
After thinking about your suggestion, Prof. Bangerth.
It came to my mind, that the result of my max_rank variable is stored on a 
specific processor due to MPI_Reduce.
That means I cannot access these data parts without being currently at the 
correspinding processor rank.
For instance I store my results on rank 0, if I want to check the max_rank 
data on processor rank 3, it is empty.
That is why I cannot get any output, because when rank 3 owns everything 
output works fine.

Now my question how can I store the data on all processors?
Or how am I able to at least store my max_rank variable on all processors?

BR,
Seyed Ali 

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