Soit une variété symplectique de dimension 2n munie dʼune action hamiltonienne du tore . Le théorème de convexité dʼAtiyah–Guillemin–Sternberg implique que lʼimage de lʼapplication moment est un polytope convexe de dimension . Dans cette Note, nous montrons que la fonction de densité de la mesure de Duistermaat–Heckman est log-concave sur lʼimage de lʼapplication moment.
Let be a closed 2n-dimensional symplectic manifold equipped with a Hamiltonian -action. Then Atiyah–Guillemin–Sternberg convexity theorem implies that the image of the moment map is an -dimensional convex polytope. In this Note, we show that the density function of the Duistermaat–Heckman measure is log-concave on the image of the moment map.
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@article{CRMATH_2012__350_17-18_845_0, author = {Cho, Yunhyung and Kim, Min Kyu}, title = {Log-concavity of complexity one {Hamiltonian} torus actions}, journal = {Comptes Rendus. Math\'ematique}, pages = {845--848}, publisher = {Elsevier}, volume = {350}, number = {17-18}, year = {2012}, doi = {10.1016/j.crma.2012.07.004}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2012.07.004/} }
TY - JOUR AU - Cho, Yunhyung AU - Kim, Min Kyu TI - Log-concavity of complexity one Hamiltonian torus actions JO - Comptes Rendus. Mathématique PY - 2012 SP - 845 EP - 848 VL - 350 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.07.004/ DO - 10.1016/j.crma.2012.07.004 LA - en ID - CRMATH_2012__350_17-18_845_0 ER -
%0 Journal Article %A Cho, Yunhyung %A Kim, Min Kyu %T Log-concavity of complexity one Hamiltonian torus actions %J Comptes Rendus. Mathématique %D 2012 %P 845-848 %V 350 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.07.004/ %R 10.1016/j.crma.2012.07.004 %G en %F CRMATH_2012__350_17-18_845_0
Cho, Yunhyung; Kim, Min Kyu. Log-concavity of complexity one Hamiltonian torus actions. Comptes Rendus. Mathématique, Tome 350 (2012) no. 17-18, pp. 845-848. doi : 10.1016/j.crma.2012.07.004. http://www.numdam.org/articles/10.1016/j.crma.2012.07.004/
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