Partitioning a convex island

This paper discusses the problem of partitioning a convex polygon C into n convex pieces such that each piece has equal area and equal length of the boundary of C: basically to divide a convex cake into convex pieces of same area and same amount of icing per piece.

Our 'fair partitioning' (spicy chicken) question (2006), a departure from the above, asks for partition of planar convex region C into convex pieces all of same area and perimeter.

Now, let us record a variant:

Given a convex planar region C to divide it into n equal area convex pieces such that each piece has the same length of cut. Basically, to parition a convex island into n convex parts, with equal length of wall needed by each piece - the coast needs no walls or fortification. Some of the portions could be landlocked.

More soon.