Here are some suggestions. I hope this produces the minimum amount of changes so the definition is equivalent to the standard terminology.

1. Instead of defining «hull», one can just state it as a «a closed curve that encloses all the points». «Hull» by itself isn't used much outside this paragraph, and one can just say «closed curve» instead of «hull» to refer to the hull because there is little ambiguity.
2. One can then define what it means for a closed curve to be convex.
3. Replace all occurrence of «minimal convex hull» with «convex hull». Define the «convex hull of S» as the region bounded by the shortest convex closed curve that contains all the points in S.
4. Finally, one can state that what it means to «find the convex hull». State it as finding the boundary curve of the convex hull(which is the original «minimal convex hull»).

One can prove this definition is equivalent to the convex hull definition for finite set of points on the plane in wikipedia.

The definition of convex hull in this article is not the same as the standard terminology. I urge the author to use the standard terminologies(which is on the wikipedia page linked in the first paragraph.)