  We investigate isoperimetric upper bounds for sums of consecutive Steklov
eigenvalues of planar domains. The normalization involves the perimeter and
scale-invariant geometric factors which measure deviation of the domain from
roundness. We prove sharp upper bounds for both starlike and simply connected
domains, for a large collection of spectral functionals including partial sums
of the zeta function and heat trace. The proofs rely on a special class of
quasiconformal mappings.
