01106nas a2200157 4500008004100000022001400041245006700055210006000122260001000182300001200192490000700204520065100211100002200862700001900884856004500903 2019 en d a1230-342900aOn the topological degree of planar maps avoiding normal cones0 atopological degree of planar maps avoiding normal cones bSISSA a825-8450 v533 a
The classical Poincaré-Bohl theorem provides the existence of a zero for a function avoiding external rays. When the domain is convex, the same holds true when avoiding normal cones.
We consider here the possibility of dealing with nonconvex sets having inward corners or cusps, in which cases the normal cone vanishes. This allows us to deal with situations where the topological degree may be strictly greater than $1$.