[Log-concavité des actions toriques hamiltoniennes de complexité un]
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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Yunhyung Cho 1 ; Min Kyu Kim 2
@article{CRMATH_2012__350_17-18_845_0, author = {Yunhyung Cho and Min Kyu Kim}, 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}, }
Yunhyung Cho; Min Kyu Kim. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.004/
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