The Gromov--Ros Conjecture in Quaternionic and Cayley Hyperbolic Geometry

We prove the unrestricted finite-perimeter Gromov--Ros conjecture in quaternionic hyperbolic spaces of dimension at least two and in the Cayley hyperbolic plane. At every positive volume, geodesic balls are the unique isoperimetric regions up to isometry and null sets. Together with the previously known real- and complex-hyperbolic cases, this completes the classification for all noncompact rank-one symmetric spaces. The proof adapts an exact-volume deformation framework to the higher long-root multiplicities arising in the quaternionic and Cayley cases. We introduce an exact volume radius, derive a uniform horizontal-vertical cofactor trace, and establish an explicit positive factorization for the relevant parameters. Minimality then forces the reduced-boundary normal to be radial almost everywhere, after which isotropy invariance and a one-dimensional weighted endpoint comparison yield the classification.