Positive-Scalar-Curvature Gluing Overview

Definitions and mathematical statement

Formulation unavailable. The supplied local registry record for permanent UnsolvedMath ID $30005853$, source code catalogue entry, contains an introduction announcing three significant open problems related to the report's construction and described as desirable next steps. It does not state any of those three problems. Consequently, no precise mathematical statement, with specified objects, hypotheses, and quantifiers, can be recovered from this record alone.

The excerpt additionally refers to an unspecified result that would ensure that the report's definition of weak concordance generalizes standard (strong) concordance and reduces to it on the distinguished subspace of metrics having positive scalar curvature and minimal boundary. This is a contextual description of the intended consequence, not a complete assertion: the result, construction, ambient manifold, space of metrics, and definitions of both concordance relations are absent. No equivalence or implication between these undefined relations is asserted in this draft.

The supplied statement status is unrecoverable. The supplied verification note says that the official report identifies this extraction as the heading and introduction to three open questions, all preserved in the following record; that following record is not included here. The registry's open label therefore does not identify a definite mathematical conjecture in this entry.

Short English statement

This entry announces three open problems but supplies none of their statements. It mentions a desired relationship between weak and strong concordance for metrics with positive scalar curvature and minimal boundary, without the definitions or hypotheses needed to formulate that relationship precisely. The missing problem statements and surrounding definitions must be recovered before mathematical formalization.

Sources

• Supplied local UnsolvedMath registry record, permanent ID $30005853$, title Positive-Scalar-Curvature Gluing Overview, exact source code catalogue entry; collection: Oberwolfach Reports Open Problems. The supplied proposed year is 2024; no individual proposer is identified.
• Supplied report citation: Analysis, Geometry and Topology of Positive Scalar Curvature Metrics (2024), Oberwolfach Reports, pp. 483--566, DOI 10.4171/owr/2024/9. Supplied source URL and literature-source link: https://doi.org/10.4171/owr/2024/9. The collection describes these reports as records of mathematical workshops and their open-problem discussions. The report is the supplied authoritative reference, but its relevant problem statements are absent from the supplied extract.
• Supplied literature assessment dated exactly 2026-08-22: status open; the extract is only a lead-in to three missing problems, so no definite claim can be assessed as solved or disproved. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. The supplied background requests independent verification of time-sensitive status and cited claims.
• Supplied statement-verification note: the official report confirms that the extraction is a heading and introduction, with the three questions preserved in the following record. This verification claim is reproduced as supplied attribution; neither the report nor that following record has been independently inspected for this draft.