Singularities of convex hulls as fronts of Legendre varieties
Banach Center Publications (1999)
- Volume: 50, Issue: 1, page 61-74
- ISSN: 0137-6934
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topBogaevski, Ilia. "Singularities of convex hulls as fronts of Legendre varieties." Banach Center Publications 50.1 (1999): 61-74. <http://eudml.org/doc/209018>.
@article{Bogaevski1999,
abstract = {We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphism. It turns out that the boundary of the convex hull is the front of a Legendre variety. Its singularities are classified up to contact diffeomorphism.},
author = {Bogaevski, Ilia},
journal = {Banach Center Publications},
keywords = {convex hulls; support hyperplanes; singularities},
language = {eng},
number = {1},
pages = {61-74},
title = {Singularities of convex hulls as fronts of Legendre varieties},
url = {http://eudml.org/doc/209018},
volume = {50},
year = {1999},
}
TY - JOUR
AU - Bogaevski, Ilia
TI - Singularities of convex hulls as fronts of Legendre varieties
JO - Banach Center Publications
PY - 1999
VL - 50
IS - 1
SP - 61
EP - 74
AB - We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphism. It turns out that the boundary of the convex hull is the front of a Legendre variety. Its singularities are classified up to contact diffeomorphism.
LA - eng
KW - convex hulls; support hyperplanes; singularities
UR - http://eudml.org/doc/209018
ER -
References
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- [2] A. B. Givental', Singular Lagrangian manifolds and their Lagrangian mappings, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Ser. Sovremennye Problemy Matematiki 33, VINITI, Moscow, 1988, 55-112 (in Russian); English transl.: J. Soviet Math. 52 (1990), 3246-3278.
- [3] V. D. Sedykh, Functional moduli of singularities of convex hulls of manifolds of codimension 1 and 2, Mat. Sb. (N.S.) 119 (1982), 233-247 (in Russian); English transl.: Math. USSR-Sb. 47 (1984), 223-236. Zbl0509.58005
- [4] V. D. Sedykh, Singularities of convex hulls, Sibirsk. Mat. Zh. 24 (1983), no. 3, 158-175 (in Russian); English transl.: Siberian Math. J. 24 (1983), 447-461. Zbl0513.58008
- [5] V. D. Sedykh, Stabilization of the singularities of convex hulls, Mat. Sb. (N.S.) 135 (1988), 514-519 (in Russian); English transl.: Math. USSR-Sb. 63 (1989), 499-505.
- [6] V. D. Sedykh, The sewing of the swallowtail and the Whitney umbrella in a four-dimensional control system, Trudy GANG im. I. M. Gubkina, Oil and Gas, Moscow, 1997, 58-68 (in Russian).
- [7] V. M. Zakalyukin, Singularities of convex hulls of smooth manifolds, Funktsional. Anal. i Prilozhen. 11 (1977), no. 3, 76-77 (in Russian); English transl.: Functional Anal. Appl. 11 (1978), 225-227.
- [8] V. M. Zakalyukin, R. M. Roberts, Stability of Lagrangian manifolds with singularities (Russian), Funktsional. Anal. i Prilozhen. 26 (1992), no. 3, 28-34; English transl.: Funct. Anal. Appl. 26 (1992), 174-178.
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