For analytic Z in R^n with dim Z ≤ n-2 and curved Σ with positive sectional or geodesic curvature, the projection π to T_x S^{n-1} satisfies dim π(Z) = dim Z for H^{n-2}-almost every x in Σ.
Restricted projections to lines inR n`1.Mathematical Proceedings of the Cambridge Philosophical Society, 179(1):105–143
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Restricted Projections to Hyperplanes in $\mathbb{R}^n$
For analytic Z in R^n with dim Z ≤ n-2 and curved Σ with positive sectional or geodesic curvature, the projection π to T_x S^{n-1} satisfies dim π(Z) = dim Z for H^{n-2}-almost every x in Σ.