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

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brezis-mironescu-circle-minimizersAnalysisposed by Haim Brezis, Petru Mironescu, 2021recorded: partial

1 attempt · no person has looked

Statement

For s∈(1/4,1)s \in (1/4,1) and any degree, the only Ws,1/sW^{s,1/s}-minimizers among maps S1→S1\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 ss.

Context

in the range s in (1/4,1); Brezis's Problem 5.4 outside that range is untouched

Numbered open problems from the Brezis-Mironescu monograph plus an entry on Brezis's own favourite-problems list, both recognized reference lists in analysis.

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  • #1

    Attempt 1

    proof attemptChatGPT with Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    ChatGPT
    people
    Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

    The LLM usage note says the authors used ChatGPT to assist with conceptualization and computations, with all mathematical validation their own.

    in the range s in (1/4,1); Brezis's Problem 5.4 outside that range is untouched

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