Geodesic
On the convex hull of several compacta
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 4, Tome 261 (1999), pp. 66-75 
A. V. Evdokimov; V. A. Zalgaller. On the convex hull of several compacta. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 4, Tome 261 (1999), pp. 66-75. http://geodesic.mathdoc.fr/item/ZNSL_1999_261_a5/
@article{ZNSL_1999_261_a5,
     author = {A. V. Evdokimov and V. A. Zalgaller},
     title = {On the convex hull of several compacta},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {66--75},
     year = {1999},
     volume = {261},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_261_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $K_0,K_1,\dots,K_m$ be nonempty compact sets in $\mathbb R^n$. Then the family of convex hulls $\operatorname{conv}\{\bigcup^m_{i=0}(K_i+r_i)\}$, $r_0=0$, is a convex family of sets, parametrized by $\rho=(r_1,\dots,r_m)\in\mathbb R^{nm}$. In case $m=1$, the volume $\operatorname{Vol\,conv}(K_0\cup(K_1+r))$ is a convex function of $r\in\mathbb R^n$.