Gromov–Hausdorff distances for polynomially defined convex bodies

Determine the Gromov–Hausdorff distance between polynomially defined convex bodies of different dimensions or with different defining parameters.

Background

The Euclidean unit balls studied in the paper are a special class of convex bodies. The authors leave unresolved the broader problem of computing or bounding Gromov–Hausdorff distances for convex bodies described by polynomial inequalities when either their dimensions or their defining parameters differ.

References

More generally, how do we determine the Gromov--Hausdorff distance between polynomially defined convex bodies of different dimensions or with different defining parameters?

— Gromov--Hausdorff Distance Between Euclidean Unit Balls  (2609.09652 - Adams et al., 9 Sep 2026) in Question, Section 6 (Conclusion and open questions)