Can men have concave profiles in rhinoplasty? Or do all men have to have a convex profile?

 Men can be born with a concave or convex profile. In most rhinoplasty procedures we  are shaving down the dorsal hump and giving a straight profile. Women tend to look better with a slightly more concave profile. Some men are born with a concave profile which can be built up with the patient's own cartilage harvested from inside the nasal septum. For many examples please see the link below

Yes, men can have a concave profile to their nose.  In general, a straight or convex profile is associated with a male face, while a concave profile is associated with female characteristics.  This is not a rule, and exceptions for both genders abound (Barbara Streisand and a younger Kevin Bacon are good examples).  The shape just changes the overall nature of the face.  The best way to see this is with computer imaging (or just try using Photoshop at home, and play with the variations!).  It really boils down to personal preference, which is why a surgeon should never tell you what nose you should have.  It is your nose you have to see every day, and you should be happy with it.

Generally an excessive concave nasal dorsum is not ideal for men or women, and is a sign of excessive removal of the bone and cartilage in a rhinoplasty. But there is a wide rage of normal, and also personal preference varies.I think a slightly concave dorsum in a male is acceptable, if he finds that attractive.