  Switchbacks are sudden and large deflections in the magnetic field that
Parker Solar Probe frequently observes in the inner heliosphere. Their
ubiquitous occurrence has prompted numerous studies to determine their nature
and origin. Our goal is to describe the boundary of these switchbacks using a
series of events detected during the spacecraft's first encounter with the Sun.
Using FIELDS and SWEAP data, we investigate different methods for determining
the boundary normal. The observed boundaries are arc-polarized structures with
a rotation that is always contained in a plane. Classical minimum variance
analysis (MVA) gives misleading results and overestimates the number of
rotational discontinuities. We propose a robust geometric method to identify
the nature of these discontinuities, which involves determining whether or not
the plane that contains them also includes the origin ($\textbf{B}=0$). Most
boundaries appear to have the same characteristics as tangential
discontinuities in the context of switchbacks, with little evidence for having
rotational discontinuities. We find no effect of the size of the Parker spiral
deviation. Furthermore, the thickness of the boundary is within MHD scales. We
conclude that most of the switchback boundaries observed by Parker Solar Probe
are likely to be closed, in contrast to previous studies. Our results suggest
that their erosion may be much slower than expected.
