Differential Geometry
Log-concavity of complexity one Hamiltonian torus actions
Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 845-848.

Let (M,ω) be a closed 2n-dimensional symplectic manifold equipped with a Hamiltonian Tn1-action. Then Atiyah–Guillemin–Sternberg convexity theorem implies that the image of the moment map is an (n1)-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.

Soit (M,ω) une variété symplectique de dimension 2n munie dʼune action hamiltonienne du tore Tn1. Le théorème de convexité dʼAtiyah–Guillemin–Sternberg implique que lʼimage de lʼapplication moment est un polytope convexe de dimension (n1). Dans cette Note, nous montrons que la fonction de densité de la mesure de Duistermaat–Heckman est log-concave sur lʼimage de lʼapplication moment.

Published online:
DOI: 10.1016/j.crma.2012.07.004
Cho, Yunhyung 1; Kim, Min Kyu 2

1 School of Mathematics, Korea Institute for Advanced Study, 87 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea
2 Department of Mathematics Education, Gyeongin National University of Education, San 59-12, Gyesan-dong, Gyeyang-gu, Incheon, 407-753, Republic of Korea
     author = {Cho, Yunhyung and Kim, Min Kyu},
     title = {Log-concavity of complexity one {Hamiltonian} torus actions},
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Cho, Yunhyung; Kim, Min Kyu. Log-concavity of complexity one Hamiltonian torus actions. Comptes Rendus. Mathématique, Volume 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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