Does there exist a compact hyperbolic 3-manifold $M$ that is not diffeomorphic to a geometrically finite hyperbolic manifold? If yes, can such $M$ have incompressible boundary?

I think the answer should be yes to both questions but I cannot find this in the literature.

**Remarks:** as usual, a *compact hyperbolic manifold* is a compact manifold whose interior carries a complete hyperbolic structure. The structure is
* geometrically finite* if it is obtained as the quotient of the hyperbolic 3-space by a geometrically finite group. Thurston's hyperbolization theorem implies:

A compact 3-manifold with non-empty boundary is hyperbolizable if and only if it is irreducible and atoroidal.

Any compact, atoroidal, pared 3-manifold is diffeomorphic to a geometrically finite one.

Any compact hyperbolic 3-manifold is homotopy equivalent to a geometrically finite one.

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