How narrowly can stone be cut for a counter?
 

I'm planning to replace the plastic laminate countertop on a center island with silestone or some other stone(-like) surface. At the same time, I'd like to install a 30" wide gas cooktop at one end (we have an electric cooktop elsewhere, but the wife would like the gas option as well). That would leave a 3"+/- edge on 3 sides of the cooktop --- supported only by the vertical cabinet walls below on the inside edge. In effect that 3" edge is cantilevered out from the cabinet.

Is this an impossible situation? Is there a stone that would be better than the others? I read that r-bar can be imbedded in silestone; might that work?

Last resort, I guess I can try to persuade my wife to go with a 24" wide cooktop.

I'm having trouble picturing this. A scale drawing may help.
I will mention you will probably regret not having any counter space directly next to your cooktop. Where will you put the mixing spoons, measuring cup, ingredient bowls, etc. etc?

and if the cooktop is installed in an island will you be using a down draft exhaust vent?

Yes, I will.

After further consideration I have decided to rotate the cooktop 90 degrees, which will alleviate the edge problem and provide the work space.