Brezis-Mironescu Open Problems 23 and 24 on Minimizing Maps to the Circle

For $s \in (1/4,1)$ and any degree, the only $W^{s,1/s}$-minimizers among maps $\mathbb{S}^1 \to \mathbb{S}^1$ are Blaschke products. This resolves Open Problems 23 and 24 of Brezis and Mironescu's book on mappings to the circle, and Brezis's Favorite Open Problem 5.4 in the same range of $s$.

Result

Proved(see note)

Status

Partial result

AI contribution

AI-assisted

Method

Argument

Field

Calculus of variations

Posed by

Haim Brezis, Petru Mironescu

Year posed

2021

Years open

5y

Solved

2026-06-14

Model

ChatGPT

Vendor

OpenAI

Collaborators

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

Verification

Unreviewed

Publication

Preprint

Significance

25 / 100*

Disclosed cost

—

Wikipedia

No dedicated article