The no-cylinder conjecture for embedded self-shrinkers

A self-shrinker is a complete embedded shrinker for mean curvature flow. The no-cylinder conjecture. The only complete embedded shrinker with a cylindrical end is the round cylinder. The source explicitly notes that it may be better regarded as a question because no convincing heuristics are known. A resolution would imply, together with prior work, a dichotomy between conical-type and neck-type singularities; the statement becomes false without completeness or embeddedness.