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An exact Lagrangian submanifold $L$ in the symplectization of standardcontact $(2n-1)$-space with Legendrian boundary $\Sigma$ can be glued to itselfalong $\Sigma$. This gives a Legendrian embedding $\Lambda(L,L)$ of the doubleof $L$ into contact $(2n+1)$-space. We show that the Legendrian isotopy classof $\Lambda(L,L)$ is determined by formal data: the manifold $L$ together witha trivialization of its complexified tangent bundle. In particular, if $L$ is adisk then $\Lambda(L,L)$ is the Legendrian unknot.

Lagrangian fillings and complicated Legendrian unknots