A generalization of the total mean curvature
Rendiconti del Seminario Matematico della Università di Padova, Tome 146 (2021), pp. 223-231.
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We derive a special formula for the total mean curvature of an ovaloid. This formula allows us to extend the notion of the mean curvature to the class of boundaries of strictly convex sets. Moreover, an integral formula is proved.

Publié le :
DOI : 10.4171/rsmup/87
Classification : 53, 52 
@article{RSMUP_2021__146__223_0,
     author = {Katarzyna Charytanowicz and Waldemar Cie\'slak and Witold Mozgawa},
     title = {A generalization of the total mean curvature},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {223--231},
     volume = {146},
     year = {2021},
     doi = {10.4171/rsmup/87},
     mrnumber = {4349655},
     zbl = {1497.53012},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/87/}
}
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Katarzyna Charytanowicz; Waldemar Cieślak; Witold Mozgawa. A generalization of the total mean curvature. Rendiconti del Seminario Matematico della Università di Padova, Tome 146 (2021), pp. 223-231. doi : 10.4171/rsmup/87. http://www.numdam.org/articles/10.4171/rsmup/87/

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