On the local meromorphic extension of CR meromorphic mappings

Let M be a generic CR submanifold in ${\displaystyle {ℂ}^{m+n}}$, m = CR dim M ≥ 1, n = codim M ≥ 1, d = dim M = 2m + n. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple ${\displaystyle (f{,}_f,\left[{\Gamma }_f\right])}$, where: 1) ${\displaystyle f{:}_f\to Y}$ is a ¹-smooth mapping defined over a dense open subset ${\displaystyle \_f}$ of M with values in a projective manifold Y; 2) the closure ${\displaystyle {\Gamma }_f}$ of its graph in ${\displaystyle {ℂ}^{m+n}\times Y}$ defines an oriented scarred ¹-smooth CR manifold of CR dimension m (i.e. CR outside a closed thin set) and 3) ${\displaystyle d\left[{\Gamma }_f\right]=0}$ in the sense of currents. We prove that ${\displaystyle (f{,}_f,\left[{\Gamma }_f\right])}$ extends meromorphically to a wedge attached to M if M is everywhere minimal and ${\displaystyle ^\omega }$ (real-analytic) or if M is a ${\displaystyle ^\{2,\alpha \}}$ globally minimal hypersurface.