Mathematicians have discovered a 'lumpy' version of a sphere that can shrink perfectly uniformly, disproving the long-held belief that only perfectly round shapes could do so.
April 1, 2026
Original Paper
Examples of compact embedded mean convex $λ$-hypersurfaces
arXiv · 2603.29371
The Takeaway
For decades, it was conjectured that the only shape capable of maintaining its proportions while collapsing under surface tension was a perfect, round ball. This discovery of a non-round, potato-like bubble that also shrinks perfectly uniformly challenges our fundamental understanding of geometric stability in physics.
From the abstract
There is a well-known conjecture asserts that the round sphere should be the only compact embedded self-shrinker (i.e. $0$-hypersurface) which is diffeomorphic to a sphere. S. Brendle confirmed the conjecture for 2-dimensional $0$-hypersurfaces. For any dimensional $\lambda$-hypersurfaces, if $\lambda 0$, we construct a compact mean convex embedded $\lambda$-hypersurface which is diffeomorphic to a sphere and is not a round sphere. In fact, for $\lambda>0$, there are no compact convex embedded $