Log-concavity of complexity one Hamiltonian torus actions

Cho, Yunhyung; Kim, Min Kyu

doi:10.1016/j.crma.2012.07.004

Differential Geometry

Log-concavity of complexity one Hamiltonian torus actions

Presented by: the Editorial Board

¹School of Mathematics, Korea Institute for Advanced Study, 87 Hoegiro, Dongdaemun-gu, Seoul, 130-722, Republic of Korea
²Department of Mathematics Education, Gyeongin National University of Education, San 59-12, Gyesan-dong, Gyeyang-gu, Incheon, 407-753, Republic of Korea

Comptes Rendus. Mathématique, Volume 350 (2012) no. 17-18, pp. 845-848

Abstract (Original language)
Résumé

Let $(M, ω)$ be a closed 2n-dimensional symplectic manifold equipped with a Hamiltonian $T^{n - 1}$ -action. Then Atiyah–Guillemin–Sternberg convexity theorem implies that the image of the moment map is an $(n - 1)$ -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 $T^{n - 1}$ . Le théorème de convexité dʼAtiyah–Guillemin–Sternberg implique que lʼimage de lʼapplication moment est un polytope convexe de dimension $(n - 1)$ . Dans cette Note, nous montrons que la fonction de densité de la mesure de Duistermaat–Heckman est log-concave sur lʼimage de lʼapplication moment.

Received: 2012-05-31
Accepted: 2012-07-11
Published online: 2012-09-01

DOI: 10.1016/j.crma.2012.07.004

Author's affiliations:

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

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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

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