  We provide a complete classification of Teichm\"uller curves occurring in
hyperelliptic components of the meromorphic strata of differentials. Using a
non-existence criterion based on how Teichm\"uller curves intersect the
boundary of the moduli space we derive a contradiction to the algebraicity of
any candidate outside of Hurwitz covers of strata with projective dimension one
and Hurwitz covers of zero residue loci in strata with projective dimension
two.

Algebraic Geometry;Dynamical Systems;Geometric Topology