Lin’s interior mass-bound problem
Determine whether, for every dimension and every algebraic projection multiplicity , there exists a constant such that every confined area-minimizing rectifiable current in Euclidean space satisfying Lin’s confinement and projection hypotheses has interior mass bounded by , without assuming any a priori mass bound at a larger scale; equivalently, whether holds in this setting.
References
Primary source
Additional references
Progress summary
An unrefereed preprint claims to solve Lin’s interior mass-bound problem and improve a related application.
Lin’s problem asks for an interior mass estimate for confined area-minimizing currents without assuming a larger-scale mass bound. No proposer or original date is identified in the retrieved material.
September 2026 claimed solution
The preprint Mass Bounds for Confined Area-Minimizing Minimal Surfaces claims an interior bound of the form without a larger-scale mass bound, and removes a doubly exponential local mass-growth hypothesis in an application. The result is reported as an unrefereed preprint, so the claimed resolution remains unverified.
Current status (as of September 2026): A preprint claims the problem is solved by proving an interior bound of the form , but the claim has not been independently verified; no contrary result was found.
Sources
- arxiv.org
- www-cdn.anthropic.com
- deepmind.google
- quantamagazine.org
- anthropic.com
- quantamagazine.org
- quantamagazine.org
- www-cdn.anthropic.com
- scientificamerican.com
- export.arxiv.org
- arxiv.org
- arxiv.org
- ar5iv.labs.arxiv.org
- arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- cdn.openai.com
- cdn.openai.com
- cdn.openai.com
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