  Border indentations in non-linear conductors, such as superconducting thin
films in the creep regime, alter the distribution of currents and magnetic
fields near and far from the indentation. One of such disturbances are the
discontinuity lines, or \textit{d}-lines, a parabolic-like line originating
from the indentation where the current density direction changes abruptly.
Hodograph series results are obtained for the currents around a triangular
indentation and its corresponding $d$-lines in a conducting stripe of finite
width and in an infinite half plane, considering two cases: uniform creep
exponent and mixed infinite and ohmic exponents. The mixed creep exponent case
presents currents distributions resembling the purely ohmic case, with
significant current disturbances only near the indentation. For uniform creep
exponent, results similar to a planar indentation are obtained, with far ranged
currents features and parabolic-like $d$-lines with shapes depending on the
creep exponent. In particular, the same $d$-line asymptotic behaviour is
obtained for the triangle indentation as that of the planar defect in the
critical state, a result obtained here just on continuity considerations of the
hodograph expansions. This equivalence is due to identical contributions to the
Fourier series of the current stream-function in the hodograph space, obtained
from an images method expansion.
