  We prove uniqueness of ground states $Q$ in $H^{1/2}$ for pseudo-relativistic
Hartree equations in three dimensions, provided that $Q$ has sufficiently small
$L^2$-mass. This result shows that a uniqueness conjecture by Lieb and Yau in
[CMP 112 (1987),147--174] holds true at least under a smallness condition.
  Our proof combines variational arguments with a nonrelativistic limit, which
leads to a certain Hartree-type equation (also known as the Choquard-Pekard or
Schroedinger-Newton equation). Uniqueness of ground states for this limiting
Hartree equation is well-known. Here, as a key ingredient, we prove the
so-called nondegeneracy of its linearization. This nondegeneracy result is also
of independent interest, for it proves a key spectral assumption in a series of
papers on effective solitary wave motion and classical limits for
nonrelativistic Hartree equations.
