Volume increasing isometric deformations of polyhedra
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 1, pp. 60-70 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We prove that any bounded polyhedron in 3 dimensional space can be isometrically deformed so as to enclose greater volume.
@article{ZVMMF_2010_50_1_a6,
     author = {G. A. Samarin},
     title = {Volume increasing isometric deformations of polyhedra},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {60--70},
     year = {2010},
     volume = {50},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a6/}
}
TY  - JOUR
AU  - G. A. Samarin
TI  - Volume increasing isometric deformations of polyhedra
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 60
EP  - 70
VL  - 50
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a6/
LA  - en
ID  - ZVMMF_2010_50_1_a6
ER  - 
%0 Journal Article
%A G. A. Samarin
%T Volume increasing isometric deformations of polyhedra
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 60-70
%V 50
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a6/
%G en
%F ZVMMF_2010_50_1_a6
G. A. Samarin. Volume increasing isometric deformations of polyhedra. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 1, pp. 60-70. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_1_a6/

[1] Aleksandrov A. D., Vypuklye mnogogranniki, Gostekhteorizdat, M.–L., 1950 | MR

[2] Aleksandrov V. A., “Kak smyat paket ot moloka, chtoby v nego voshlo bolshe”, SOZh, 2000, no. 2, 121–127

[3] Bleecker D. D., “Volume increasing isometric deformation of convex polyhedra”, J. Different. Geometry, 1996, no. 43, 505–526 | MR | Zbl

[4] Samarin G. A., “Izometricheskie deformatsii mnogogrannikov, uvelichivayuschie soderzhaschiisya v nikh ob'em”, “Diskretnaya matem. i ee prilozh.”, Materialy IX mezhdunar. seminara, Izd-vo MGU, M., 2007, 406–409

[5] Burago Ju. D., Zalgaller V. A., “Isometric piecewise-linear embedding of two-dimensional manifolds with polyhedral metric into $R^3$”, St. Petersburg Math. J., 7 (1996), 369–385 | MR