knife–edge 
/ˈnaɪfˌɛʤ/ noun
/ˈnaɪfˌɛʤ/ noun [singular] : something that is very narrow or sharp
▪ The path was a knife-edge on the side of a steep hill.
▪ The path was a knife-edge on the side of a steep hill.
on a/the knife-edge
: in a dangerous or important situation in which two very different results are possible
▪ a region resting on a knife-edge after several wars ▪ The election results hung on a knife-edge. ▪ living on the knife-edge of poverty
▪ a region resting on a knife-edge after several wars ▪ The election results hung on a knife-edge. ▪ living on the knife-edge of poverty
