  Point defects are ubiquitous in two dimensional crystals and play a
fundamental role in determining their mechanical and thermodynamical
properties. When crystals are formed on a curved background, finite length
grain boundaries (scars) are generally needed to stabilize the crystal. We
provide a continuum elasticity analysis of defect dynamics in curved crystals.
By exploiting the fact that any point defect can be obtained as an appropriate
combination of disclinations, we provide an analytical determination of the
elastic spring constants of dislocations within scars and compare them with
existing experimental measurements from optical microscopy. We further show
that vacancies and interstitials, which are stable defects in flat crystals,
are generally unstable in curved geometries. This observation explains why
vacancies or interstitials are never found in equilibrium spherical crystals.
We finish with some further implications for experiments and future theoretical
work.
