undertake something in what appears to be the easiest, quickest or cheapest way, often by omitting to do something important or ignoring rules.
This phrase comes from cutting (off) the corner which means taking the shortest course by going across and not round a corner.
the four corners of the world = the far corners of the world = the four corners of the earth = the far corners of the earth
remote regions of the earth, far away from each other
1999 - Katie Hickman - Daughters of Britannia – In amongst the fishing boats and the caiques sailed innumerable vessels from all four corners of the earth.
in his corner
on someone's side
giving someone support
This idiom and fight your corner is boxing metaphors and refers to the diagonally opposite corners taken by opponents in a boxing match. Trainers and assistants are in a boxer's corner to offer support and encouragement between rounds.
paint yourself into a corner
leave yourself no means of escape or room to maneuver