bibkey: harveylawson1982calibrated authors: Reese Harvey; H. Blaine Lawson year: 1982 title: Calibrated geometries doi: 10.1007/BF02392726 url: https://researchconnect.stonybrook.edu/en/publications/calibrated-geometries/ claim: A closed form bounded above by oriented unit volume certifies volume minimization of calibrated representatives under the appropriate homology or boundary condition. strata_touched: [] license: citation-only triage: anchor

Calibration and the FIB leakage comparison

Harvey and Lawson, Calibrated geometries, Acta Mathematica 148, 47–157. Crossref and the Stony Brook publication record agree on title, authors, publication year, pages and DOI.

The original article’s full text is not available in the retrieved material; no original theorem or page locator is attested here. An authoritative mathematical corroboration is Dominic Joyce, Lectures on Calabi–Yau and special Lagrangian geometry, https://arxiv.org/pdf/math/0108088v3, §6.2, Proposition 6.1: a compact calibrated submanifold is volume-minimizing in its homology class. That section explicitly credits Harvey–Lawson §§I–II. Joyce’s proof uses the pairing with the closed calibration and its pointwise volume bound. It states a homology comparison, not the exact boundary formulation used by the FIB volume.

The FIB boundary volume §9 gives the required Euclidean same-oriented-boundary proof directly: its constant three-form is exact, so Stokes equates the two integrals. The leakage identity, orientation distinction and cost relation are additional explicit calculations. Calibration alone supplies neither a physical action nor a comparison between quantities with different geometric dimensions or units. The original-primary-text limitation does not substitute for a proof of those calculations.