Obviously there is a prohibition; the question is where the prohibited area is. I understood that there is discussion about the location of the prohibition.

There are many disputes about this. The Shulchan Arukh, Yoreh De’ah 181:11, writes:
The corners of the beard are five, and there are many differing opinions about them; therefore, a God-fearing person should avoid all of them and should not pass a razor over his entire beard at all. The Rema adds: even under the throat.

I found a short overview here: http://www.kipa.co.il/ask/show/105840-%D7%92%D7%99%D7%9C%D7%95%D7%97-%D7%97%D7%9C%D7%A7%D7%99-%D7%A2%D7%9D-%D7%A1%D7%9B%D7%99%D7%9F!