  We are concerned with the Calder\'on inverse inclusion problem, where one
intends to recover the shape of an inhomogeneous conductive inclusion embedded
in a homogeneous conductivity by the associated boundary measurements. We
consider the highly challenging case with a single partial boundary
measurement, which constitutes a long-standing open problem in the literature.
It is shown in several existing works that corner singularities can help to
resolve the uniqueness and stability issues for this inverse problem. In this
paper, we show that the corner singularity can be relaxed to be a certain
high-curvature condition and derive a novel local unique determination result.
To our best knowledge, this is the first (local) uniqueness result in
determining a conductive inclusions with general smooth shapes by a single
(partial) boundary measurement.
