Clarkson–Mann minimal-mass conjecture for Eguchi-Hanson-AdS data

Let $(\mathcal S,\overline{g},K)$ be initial data of Eguchi-Hanson type with

$$\mathcal S=(a,\infty)\times(S^3/\mathbb{Z}_n),$$

and let $M$ be their mass and $M_{\mathrm{EH},a}$ the mass of the Eguchi-Hanson-AdS spacetime with parameter $a$.

Clarkson–Mann conjecture. The mass satisfies

$$M\geq M_{\mathrm{EH},a},$$

with equality if and only if the data agree with those induced by the Eguchi-Hanson-AdS spacetime with parameter $a$.

This conjecture asserts that Eguchi-Hanson-AdS has minimal mass among the relevant asymptotically locally AdS data. The paper proves the corresponding strict mass gap for sufficiently small nonzero perturbations, but not the full global statement.