FreeMind does not open

I have some files created with the mindmap-app FreeMind.
Now, when I want to open those files on a new computer, FreeMind does install but will not open.
I cannot find a clear answer to why, but it might be related to some issues with java runtime environment, of which I have no understanding.

I get no error messages or warning, the app just does not open.

Is there a way to figure out, what the problem might be?