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複素解析幾何セミナー
過去の記録 ～06/26｜次回の予定｜今後の予定 06/27～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
2017年10月16日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
須川 敏幸 氏 (東北大学)
Characterizations of hyperbolically k-convex domains in terms of hyperbolic metric
須川 敏幸 氏 (東北大学)
Characterizations of hyperbolically k-convex domains in terms of hyperbolic metric
[ 講演概要 ]
It is known that a plane domain X with hyperbolic metric hX=hX(z)|dz| of constant curvature −4 is (Euclidean) convex if and only if hX(z)dX(z)≥1/2, where dX(z) denotes the Euclidean distance from a point z in X to the boundary of X. We will consider spherical and hyperbolic versions of this result. More generally, we consider hyperbolic k-convexity (in the sense of Mejia and Minda) in the same line. A key is to observe a detailed behaviour of the hyperbolic density hX(z) near the boundary.
It is known that a plane domain X with hyperbolic metric hX=hX(z)|dz| of constant curvature −4 is (Euclidean) convex if and only if hX(z)dX(z)≥1/2, where dX(z) denotes the Euclidean distance from a point z in X to the boundary of X. We will consider spherical and hyperbolic versions of this result. More generally, we consider hyperbolic k-convexity (in the sense of Mejia and Minda) in the same line. A key is to observe a detailed behaviour of the hyperbolic density hX(z) near the boundary.
