The Minkowski Sum of two subsets $A,B \subset \mathbb{R}^n$ is $$A \oplus B = \{a + b | a \in A, b \in B\}$$ For a given $A$, is there some condition that tells me when I can find a $B$ such that $A = B \oplus B$?
For a specific example/context I was thinking about, let $K = $filled in Koch Snowflake in $\mathbb{R}^2$. Then, $K \oplus K = $filled in hexagon. This is not too surprising given that there is theorem saying $\frac{1}{n} (A + \cdots n \text{ times} \cdots + A) \to \text{Convex Hull}(A)$, so $K$ is like half a hexagon (and perhaps, it is the 'smallest' half a hexagon, if you drop the filled-in-ness of it, up to a measure 0 set?). Is there something that is half of $K$?