Workshop Summary on Geometric Measure Theory and Flows

Definitions and mathematical statement

Unrecoverable mathematical statement. The supplied record begins with the isolated word "conjecture," whose antecedent is absent, and continues with workshop-summary prose. It contains no identifiable standalone conjecture with specified objects, hypotheses, domains, boundary conditions, quantifiers, and conclusion. Consequently, no precise mathematical statement or associated system of definitions can be recovered from this evidence without inventing missing content or selecting an unsupported target.

The passage attributes the following topics and reported results to workshop speakers; these descriptions are retained as source context, not asserted here as verified mathematical results:

• Salvatore Stuvard: fine properties of singular sets of area-minimizing currents modulo $p$, in both the hypersurface and general-codimension settings. The passage does not specify the admissible values of $p$ or a proposed assertion.
• Zihui Zhao: an estimate for the Hausdorff measure of the singular set of a harmonic function in terms of Almgren's frequency function near the boundary. The domain, boundary hypotheses, definition of the singular set, and estimate are absent.
• Alessandra Pluda: asymptotic behavior and restarting procedures for network curvature flow.
• Felix Schulze: a reported uniqueness result for tangent flow of rational Lagrangian mean curvature flow, described as allowing continuation past a singularity; the meaning of "rational" and the continuation hypotheses are unspecified.
• Luca Spolaor: fine regularity at a branch point in the two-dimensional Bernoulli problem, using quasiconformal maps and the hodograph transformation.
• Mariana Smit Vega Garcia: results on a fractional free-boundary problem of Alt--Caffarelli--Friedman (ACF) type.
• Denis Kriventsov: a reported integral estimate for deviation of the first Laplacian eigenfunction on the unit ball in terms of eigenvalue deviation, with an application to the ACF problem. The comparison objects, normalization, boundary conditions, and estimate are not given.
• Xavier Lamy and Andrew Lorent: progress on the Aviles--Giga conjecture and fine-scale regularity and rigidity of elements of the Aviles--Giga space; neither the conjecture nor the space is defined in the passage.
• Filip Rindler: a stated need for a new duality and slicing theory for transport of currents, without a specific mathematical assertion.
• Daniel Faraco and André Guerra: progress on Morrey's conjecture concerning quasiconvexity, focusing on the Burkholder functional; no particular formulation, functional, or hypotheses are supplied.
• Annalisa Massaccesi and Jonas Hirsch: the role of geometric integrability and nonintegrability, described through Hörmander versus Frobenius conditions, in regularity; Massaccesi's setting is submanifolds, and Hirsch's is the De Giorgi--Nash--Moser theorem.

The passage also mentions regularity issues and constraints on oscillatory behavior generally. None of these descriptions uniquely determines the intended problem. The registry supplies the status label open while marking the statement unrecoverable; the former is supplied classification, not a verified open-problem assertion.

Short English statement

This entry preserves an incomplete extraction from a workshop summary. It lists several research topics and reported results, but gives no definite conjecture to formalize. Recovering the intended claim and its hypotheses requires human source review; choosing one of the named topics would be unsupported.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30005202$, exact source problem code catalogue entry, titled "Workshop Summary on Geometric Measure Theory and Flows," in the Oberwolfach Reports Open Problems collection. No individual problem proposer is supplied.
• Supplied source citation: Calculus of Variations (2023), Oberwolfach Reports, DOI 10.4171/owr/2022/37, pp. 2129--2193. Supplied source URL and literature-source link labeled "original Oberwolfach report": https://doi.org/10.4171/owr/2022/37. This report-level reference supplies provenance, but the record gives no authoritative citation to a recoverable standalone problem.
• The registry supplies proposed year $2022$ and tag owr-year:2022, whereas its bibliographic citation uses $2023$. These year designations are preserved without resolving their relationship.
• Literature assessment dated exactly 2026-08-22: the supplied curation labels the entry "open" and says that the extracted word "conjecture" followed by workshop-summary prose yields no definite mathematical claim that can be verified. This is supplied dated curation, not an independently verified literature assessment. The background explicitly requests independent verification of time-sensitive status and cited claims.
• The supplied statement-verification field reports that the official report confirms the passage is workshop-summary prose and a list of topics, rather than a standalone mathematical problem. It states that no separate clean statement is promoted and that the original record remains publicly visible for provenance. This verification report is supplied metadata; no source visit or independent verification is claimed here.
• Speaker attribution is retained in the contextual list above. The passage also acknowledges the MFO and workshop organizers and National Science Foundation support for junior researchers through grant DMS-1641185, "US Junior Oberwolfach Fellows."