Every dulcimer will have its own fingerboard 'profile,' meaning a concave 'dish', though some makers prefer to build with a flat fingerboard, I hear.
Dwain, could you please explain this more, I was not aware of this. I have only built with flat fingerboards so I'm having a hard time understanding what you mean by 'concave dish.'
Some builders do build flat fretboards. When there are as many frets as the dulcimer has, though, the problem of getting the lowest action becomes very much like that of designing auditorium seating.
Imagine an auditorium in which the seating floor is flat: even if everyone is the same height, people will have trouble seeing over the heads of those in the next row. And in the foremost rows (that cost the most to get), you begin to see less and less of the performers!
So the answer is to make the floor a long sweeping curved surface sloping gently down, each row a little lower than the one behind. That works well until about 2/3 down toward the stage: at that point the person in the next row are no longer the issue. Now the problem is that you can't see all of what's happening on-stage. So the floor has to start to rise so each row is a bit higher than the one before. Then each person can see everything on the stage.
So think of the string's "line of sight" as it is fretted at each fret, and design your fretboard so that, at each fret position, the height above the further frets is equal. If you're good at trigonometry you can solve the problem as one of the string forming a constant angle when fretted at each angle such that the sine of the angle is just a bit greater than the top of the next fret's crown. Since the distance between frets is exponential, that fretboard surface will be very interesting mathematically. (I've never done it mathematically. I prefer the heuristic method in instrument building, not analytics —except in the matter of setting frets in equal temperament).