Not to be argumentative, but...
How could that be true if development is time and temperature dependent, among other things?
While I agree that development is incomplete, the problem is that the edges have received more development than the middle. The same problem can occur by using a tray to small for a sheet of film such that the turbulence at the sides of the tray cause uneven development.
Again, not wanting to start an argument, but please explain.
Regardless of time and temperature, the film has not been developed long enough. Perhaps "incomplete" development is a bad word to use, since, as Nicholas sez, all continuous tone results are "incomplete". What I meant was incomplete in terms of what was expected from the film in this scenario, not incomplete in terms of what density the film is capable of achieving. (If one wants to play that game, no piece of film has been completely developed until every bit of exposed silver on the whole sheet is maximum black.) Let me say "too short" a development time instead. A sheet of film in a tray starts developing like this with constant agitation this way and that way. You can see it on litho film in developer and the fixer. If you extend development time so that the period of time that it is uneven at the edges becomes a smaller percentage of the total developing time, and/or slow your agitation routine, and/or just let the film stand, and/or entirely lift and drain the sheet, it is not noticeable on the film. When I said development was not complete, what I meant was that the middle of the film had not yet developed, though the edges had. It is a given that the edges have received more development than the middle...that was the clue that led to the idea of developing time being too short.
For what it is worth, my developing times for continuous tone on this film are in the three to five minute range (with HC or LC-1), and I use a long pre soak. For halftone results, one minute in AB developer finishes the film pretty well, though I usually do two anyhow.
Another issue is that film exhausts your chemicals very quickly compared to paper. I always used my HC one shot (or two shot), and have to replace my fixer very frequently according to the hypo check drops. I'm supposed to get about 25 8x10s-worth of film from my Liter of fixer, which should be 50 5x7s plus test strips. I get about a quarter of that before the fixer loads up with silver using litho film, however. I imagine that it similarly kills developers quite quickly.
Also for what it is worth, I develop all my in-camera sheet film in trays the same way I develop litho film, and the edges are not more dense than the middles, except with very short development times. (Attempting to test for N-2 with D-76 stock solution is one specific example that I remember, ad even then, it was only really noticeable with a densitometer.)