Sharp Euclidean moment-curve extension constants and maximizers

Determine the optimal constant and characterize all maximizers for the Euclidean restriction/extension inequality associated with the moment curve in every dimension.

Background

The paper contrasts its finite-field result with the Euclidean restriction theory for the moment curve. It states that, although existence of maximizers and sharp estimates for monomial curves are known in certain forms, the exact sharp constant for the Euclidean moment curve remains undetermined in every dimension and the corresponding maximizers have not been identified.

References

There, however, the optimal constant is not known in any dimension: Biswas and Stovall established the existence of maximizers and obtained sharp restriction estimates for monomial curves, but the maximizers themselves remain elusive.

— Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution  (2609.29882 - Biswas et al., 24 Sep 2026) in Section 1, Introduction and statement of results