  We study minimal area world sheets ending on two concentric circumferences on
the boundary of Euclidean $AdS_{3}$ with mixed R-R and NS-NS three-form fluxes.
We solve the problem by reducing the system to a one-dimensional integrable
model. We find that the NS-NS flux term either brings the surface near to the
boundary or separates the circumferences. In the limit of pure NS-NS flux the
solution adheres to the boundary in the former case and the outer radius
diverges in the latter. We further construct the underlying elliptic spectral
curve, which allows us to analyze the deformation of other related minimal
surfaces. We show that in the regime of pure NS-NS flux the elliptic curve
degenerates.
