R.Munafo: If the annulus is acceptable as a 2-D solution (mentioned earlier in this discussion), then your annular torus would have to be acceptable in 3-D too. I don't think either should count. It has to be actually physically viable for fertilizer purposes.

--well, ok. Stimulated by this complaint, it occurred to me (somewhat contrary to my mistaken claim before) that there is a 2D solution under Munafo's rules. Start with a star-shaped object S as in a previous post where the angle-condition equation was given for constant surface. Let said object erode for some timespan T>0 yielding smaller object S' with same topology. Now the object S-S' works: it will erode maintaining constant surface for 0<t<T, then instantly vanish. If star is mirror-symmetric then I also think we can make this 3D by torifying it -- torus with hollow-star cross section -- which would be a nice solution to my original problem! Further, with Munafo's attitude, if we demand S have SMOOTH measurable boundary, then I can prove no 2D solution exists. Here is proof sketch. Munafo is only permitting 2D shapes with the topology of a disk (or union of disjoint disks). Well, I suppose he would permit holes, but there are effectively no holes until such time as the erosion eliminates them by making them become exterior suddenly. If this sudden transition occurs on just part of the hole-boundary then we get a discontinuous increase-jump in surface, and game over, we lose. If it occurs on all of it simultaneously, then also discontinuous jump (now decrease) and we still lose, unless that instant was the final instant when the whole shape vanishes. OK, so, effectively during the timespan of existence of object, no holes exist. In that case by the Gauss-Bonnet theorem (which in 2D is a rather trivial statement) the total curvature of the boundary o is 2*pi radians, which means that after infinitesimal erosion time dt, the boundary shrinks by subtraction of 2*pi*dt from its length. (We only need this to work throughout an arbitrarily short time-interval.) But that contradicts constancy. Q.E.D. Objection to proof: the jump-decrease could be designed to cancel a jump-increase of exactly same size. Counter to objection: So what? You still are killed by the Gauss-Bonnet argument during timespan before the first hole is uncovered. You could make an infinite set of holes so that we get uncovering infinitely often, but that would not work since you'd need an UNCOUNTABLE infinity of holes, which'd contradict measurable boundary, or something, dammit. You also can use 3D Gauss-Bonnet theorem to see no 3D object with topology of a ball and smooth boundary can work... which is why my secret alleged messy 3D solution does have smooth boundary, but does not have the topology of a set of disjoint balls.