Connection between heavenly and earthly judgment
What is the connection between the heavenly court above and the court below on Rosh Hashana?
I am not sure I understand the question. I would just mention that the midrash says that when there is judgment below, there is no judgment above in heaven. The commentaries explain this to mean that if a person judges himself and examines his deeds and repents them, then the heavenly court will not judge him because he has already judged himself and fixed his behavior.