I have this: a plane, as you can see.
And a Curve:
When I try to create a rolling mat effect, using the curve modifiers, the plan is deform like this:
What I want is to keep the mat dimensions. Thanks.
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Check the radius of each control point of your curve and set them to 1. You can select all of them and set the "mean radius".
Most likely you scaled down or up your curve then applied the transform. This actually keeps the curve at the same position but changes the radius of each control point.
Note : You can deactivate the use of the radius of control points altogether by toggling "radius" in the curve properties. That means any deformation using this curve will consider every control point with a radius of 1 :