Do you have some specific examples? I read half of the PDF but I don’t have knowledge of case laws that would be relevant.

This headline is wrong. The DOJ is alleging that they are being anticompetitive in the Performance Smartphone market, and further that their anticompetitive behavior affects even the regular smartphone market.

The document published by the DOJ make the point that Apple has closer to 65% market share of you to by revenue, and also have a high market share amoung the teens. But I don’t get this focus on whether or not Apple is a monopoly. The lawsuit alleges that Apple has a significant market share is using anticompetitive practices to stay there.