  We investigate deformations of extremal near-horizon geometries in
Einstein-Maxwell-Dilaton theory, including various topological terms, and also
in D=11 supergravity. By linearizing the field equations and Bianchi identities
over the compact spatial cross-sections of the near-horizon geometry, we prove
that the moduli associated with such deformations are constrained by elliptic
systems of PDEs. The moduli space of deformations of near-horizon geometries in
these theories is therefore shown to be finite dimensional.
