Relative equilibria with holes for the surface quasi-geostrophic equations

We study the existence of doubly connected rotating patches for the inviscid surface quasi-geostrophic equation left open by de la Hoz, Hassainia and Hmidi in 2016 in [10]. By using the approach proposed in 2016 by Castro, Córdoba and Gomez-Serrano in [4] we also prove that close to the annulus the boundaries are actually analytic curves.