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タイトル UPPER BOUNDS FOR HIGHER-ORDER POINCARE CONSTANTS 2019年10月15日 16:30～18:00 船野　敬　氏　(東北大学) 矢上キャンパス14-733（14棟7階ミーティング3） We introduce higher-order Poincaré constants for compact weighted manifolds and estimate them from above in terms of subsets. These estimates imply upper bounds for eigenvalues of the weighted Laplacian and the first nontrivial eigenvalue of the p-Laplacian. In the case of the closed eigenvalue problem and the Neumann eigenvalue problem these are related with the estimates obtained by Chung-Grigor’yan-Yau and Gozlan-Herry. We also obtain similar upper bounds for Dirichlet eigenvalues and multi- way isoperimetric constants. As an application, for manifolds with boundary of non-negative dimensional weighted Ricci curvature, we give upper bounds for inscribed radii in terms of dimension and the first Dirichlet Poincare constant. Joint work with Yohei Sakurai.