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1. noun A stressful situation or mindset. I am on a knife-edge right now, waiting to hear if my contract has been extended—if not, I'll need to find a new job. Our grandmother is very ill, so we are all on a knife-edge these days.
2. adjective Very crisply and neatly folded. Typically said of the pleats of a garment or textile. When you fold that tablecloth, I need to see knife-edge pleats in it! That dry-cleaner does a great job getting a knife-edge crease in my pants.
3. adjective Sharp, narrow, and hard to traverse. Typically said of topographic features, like mountains. That knife-edge mountain pass has 1,000-foot drops on either side.