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

Analysis · posed by Haim Brezis, Petru Mironescu, 2021 · partial

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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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Dorian Martino, Katarzyna Mazowiecka and Armin Schikorra, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai assisted
    — a person led the work and used a model along the way.

    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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Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

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