Abstract
A cooriented circle immersion into the plane can be extended to a stable map of the disk which is an immersion in a neighborhood of the boundary and with outward normal vector field along the boundary equal to the given coorienting normal vector field. We express the minimal number of fold components of such a stable map as a function of its number of cusps and of the normal degree of its boundary. We also show that this minimum is attained for any cooriented circle immersion of normal degree not equal to one.
Funding Statement
The first author is a research fellow of the Royal Swedish Academy of Sciences sponsored by the Knut and Alice Wallenberg foundation.
Citation
Tobias Ekholm. Ola Larsson. "Minimizing singularities of generic plane disks with immersed boundaries." Ark. Mat. 43 (2) 347 - 364, October 2005. https://doi.org/10.1007/BF02384784
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