We derive local
estimates for complete noncompact translating solitons of the Gauss curvature flow
in which are graphs over a
convex domain
. This is closely
is related to deriving local
estimates for the degenerate Monge–Ampère equation. As a result, given a weakly convex bounded
domain
, we establish
the existence of a
translating soliton. In particular, when the boundary
has
line segments, we show the existence of flat sides of the translator from a local
a priori nondegeneracy estimate near the free boundary.
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