Will Christians be present on the earth at the time the anti-Christ appears? Does the anti-Christ appear before or after the Rapture?
It depends on your definitions of a couple of terms. If by Christians, you mean post-Church believers, then yes, there will be many on Earth when the anti-Christ appears. As for the anti-Christ, some scholars believe he’s alive today, so in that sense he has appeared on Earth, although no one knows who he is.
But 2 Thes. 2:7 says that he won’t be allowed to release his secret power of lawlessness until the restrainer is taken out of the way. The Restrainer is widely held to be the Holy Spirit resident in the Church. So his official introduction to the world can’t take place until after the Rapture.