Scalar--Mean Rigidity for Hyperbolic Balls in Dimensions $2\le n\le 5$

In this paper, we prove the non-spin hyperbolic scalar–mean rigidity theorem in dimensions $2\le n\le 5$, resolving the corresponding low-dimensional case of a problem of Gromov. The proof combines the Jang deformation with capillary $\mu$-bubble dimension reduction. We also establish weighted scalar–mean rigidity for Euclidean ball–torus products in total dimension at most seven and show that its hyperbolic analogue fails.