Geodesic
Smoothness of the signed distance function: A simple proof
The Teaching of Mathematics, XXVI (2023) no. 1, p. 14
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The paper is of pedagogical nature and is aimed mainly at students. It presents a detailed proof of the well-known fact that if the boundary of an open set in ${R}^n$ is of class $C^k$, $k\geq 2$, so is the signed distance to the boundary function. This function plays an important role in problems of Analysis and Geometry. The presented proof could give a teacher a good opportunity to discuss important theorems in Calculus.
DOI : 10.57016/TM-DVLA5418
Classification : 97I40, 58C07, 26B05 I45
Keywords: signed distance function, smooth boundary. 
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Johann Davidov. Smoothness of the signed distance function: A simple proof. The Teaching of Mathematics, XXVI (2023) no. 1, p. 14 . doi: 10.57016/TM-DVLA5418

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