The gradient map associated to a regular open convex cone gives
a diffeomorphism from the cone onto its dual cone.
If the cone is homogeneous, the inverse of the map is known to be equal
to the gradient map associated to the dual cone.
However, we show that this is no longer true for a general case
by presenting a simple counterexample.
Publié le : 2005-03-14
Classification:
Regular open convex cone,
dual cone,
gradient map,
52A20,
53A15,
52A15
@article{1116442035,
author = {Ishi, Hideyuki},
title = {The gradient maps associated to certain non-homogeneous cones},
journal = {Proc. Japan Acad. Ser. A Math. Sci.},
volume = {81},
number = {3},
year = {2005},
pages = { 44-46},
language = {en},
url = {http://dml.mathdoc.fr/item/1116442035}
}
Ishi, Hideyuki. The gradient maps associated to certain non-homogeneous cones. Proc. Japan Acad. Ser. A Math. Sci., Tome 81 (2005) no. 3, pp. 44-46. http://gdmltest.u-ga.fr/item/1116442035/