Geodesic
Smoothness of the signed distance function: A simple proof
The Teaching of Mathematics, XXVI (2023) no. 1, p. 14 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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. 
@article{10_57016_TM_DVLA5418,
     author = {Johann Davidov},
     title = {Smoothness of the signed distance function: {A} simple proof},
     journal = {The Teaching of Mathematics},
     pages = {14 },
     publisher = {mathdoc},
     volume = {XXVI},
     number = {1},
     year = {2023},
     doi = {10.57016/TM-DVLA5418},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.57016/TM-DVLA5418/}
}
TY  - JOUR
AU  - Johann Davidov
TI  - Smoothness of the signed distance function: A simple proof
JO  - The Teaching of Mathematics
PY  - 2023
SP  - 14 
VL  - XXVI
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.57016/TM-DVLA5418/
DO  - 10.57016/TM-DVLA5418
LA  - en
ID  - 10_57016_TM_DVLA5418
ER  - 
%0 Journal Article
%A Johann Davidov
%T Smoothness of the signed distance function: A simple proof
%J The Teaching of Mathematics
%D 2023
%P 14 
%V XXVI
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.57016/TM-DVLA5418/
%R 10.57016/TM-DVLA5418
%G en
%F 10_57016_TM_DVLA5418
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. http://geodesic.mathdoc.fr/articles/10.57016/TM-DVLA5418/

Cité par Sources :