The authors construct the first rationally convex surfaces in C2 with only hyperbolic complex tangencies, in fillable and non-fillable versions.
Lagrangian Approximation of Totally Real Concordances
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abstract
We show that a two-dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we provide are constructions of knotted Lagrangian concordances in arbitrary four-dimensional symplectiations, as well as of knotted Lagrangian tori in symplectisations of overtwisted contact three-manifolds.
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Rationally Convex Surfaces with hyperbolic complex tangencies
The authors construct the first rationally convex surfaces in C2 with only hyperbolic complex tangencies, in fillable and non-fillable versions.