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arXiv · 1205.0231

Triangles on planar Jordan $C^1$-curves

Jean-Claude Hausmann
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Abstract

We prove that a Jordan $\calc^1$-curve in the plane contains any non-flat triangle up to translation and homothety with positive ratio. This is false if the curve is not $C^1$. The proof uses a bit configuration spaces, differential and algebraic topology as well as the Schoenflies theorem. A partial generalization holds true in higher dimensions.

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Jean-Claude Hausmann. 2013-02-26. Triangles on planar Jordan $C^1$-curves. https://arxiv.org/abs/1205.0231

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