Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 367. The critical dimension for the one-phase Bernoulli problem
Family claims › Partial differential equations · lines 2375–2380
OpenAI@2026-10-07#rem:oai-367
Establishes seven as the first dimension admitting a nonflat, one-homogeneous global minimizer of the one-phase Bernoulli energy. Consequently, minimizing free boundaries are smooth through dimension six, and their singular sets have dimension at most in higher dimensions.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 362. Global smoothness for relativistic Vlasov–Maxwell
- remark: Remark: Family 363. Boltzmann nonuniqueness with exact local conservation
- remark: Remark: Family 364. Kinetic limits and fluctuations over the Boltzmann lifespan
- remark: Remark: Family 365. Joint metric and connection recovery from one boundary patch
- remark: Remark: Family 366. The planar Mumford–Shah regularity conjecture
- remark: Remark: Family 368. The three-dimensional Ball–Evans approximation problem
- remark: Remark: Family 369. The hot spots conjecture for simply connected planar domains
- remark: Remark: Family 370. The subcritical Lane–Emden and Hénon–Lane–Emden conjectures