The He-Schramm conjecture asserts that a circle domain is conformally rigid iff its boundary is a conformally removable set. Rigidity means that every conformal equivalence from the domain onto another circle domain is the restriction of a Möbius transformation. Rajala (2025) disproved the rigidity-to-removability implication by constructing a rigid circle domain with non-removable boundary. This counterexample does not refute the reverse implication.
He-Schramm Conjecture
See also
Circle Domain, Conformally Removable Set, Moebius TransformationExplore with Wolfram|Alpha
References
Rajala, K. "Rigid Circle Domains with Non-Removable Boundaries." Proc. London Math. Soc. 131, e70081, 2025. https://doi.org/10.1112/plms.70081.Cite this as:
Weisstein, Eric W. "He-Schramm Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/He-SchrammConjecture.html