  Gauge-theory approach to describe Dirac fermions on a disclinated flexible
membrane beyond the inextensional limit is formulated. The elastic membrane is
considered as an embedding of 2D surface into R^3. The disclination is
incorporated through an SO(2) gauge vortex located at the origin, which results
in a metric with a conical singularity. A smoothing of the conical singularity
is accounted for by replacing a disclinated rigid plane membrane with a
hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The
embedding parameters are chosen to match the solution to the von Karman
equations. A homogeneous part of that solution is shown to stabilize the
theory. The modification of the Landau states and density of electronic states
of the graphene membrane due to elasticity is discussed.
