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Combinatorial Properties of Self-Overlapping Curves and Interior Boundaries Evans, Parker Fasy, Brittany Terese Wenk, Carola Self-overlapping curves interior boundaries minimum homotopy area immersion We study the interplay between the recently-defined concept of minimum homotopy area and the classical topic of self-overlapping curves. The latter are plane curves that are the image of the boundary of an immersed disk. Our first contribution is to prove new sufficient combinatorial conditions for a curve to be self-overlapping. We show that a curve γ with Whitney index 1 and without any self-overlapping subcurves is self-overlapping. As a corollary, we obtain sufficient conditions for self-overlapping ness solely in terms of the Whitney index of the curve and its subcurves. These results follow from our second contribution, which shows that any plane curve γ, modulo a basepoint condition, is transformed into an interior boundary by wrapping around γ with Jordan curves. In fact, we show that n+1 wraps suffice, where γ has n vertices. Our third contribution is to prove the equivalence of various definitions of self-overlapping curves and interior boundaries, often implicit in the literature. We also introduce and characterize zero-obstinance curves, a further generalization of interior boundaries defined by optimality in minimum homotopy area. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Parker Evans and Brittany Terese Fasy and Carola Wenk 2020 Is Part Of LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2020.41 urn:nbn:de:0030-drops-121993 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.41 eng https://creativecommons.org/licenses/by/3.0/legalcode