  We study the surface modes of a homogeneous spherical gain medium and provide
a comprehensive analytic treatment of a special class of these modes that
support spectral singularities. Because the latter have a divergent quality
factor, we call them the singular gallery modes. We show that they can be
excited using arbitrarily small amounts of gain, and as a result, the system
lacks a lasing threshold, effectively. This shows that we can realize spectral
singularities in the surface modes of extremely small spherical samples with
modest amounts of gain. We also examine the possibility of exciting singular
gallery modes with different wavelengths using the same amount of gain. This
corresponds to the situation where the system undergoes simultaneous lasing at
different wavelengths.
