2001 Fiscal Year Annual Research Report

CAT-空間の距離構造に関する研究

Research Project

Project/Area Number	13874012
Research Category	Grant-in-Aid for Exploratory Research
Research Institution	Saga University
Principal Investigator	塩濱勝博佐賀大学, 理工学部, 教授 (20016059)
Co-Investigator(Kenkyū-buntansha)	半田賢司佐賀大学, 理工学部, 助教授 (10238214) 三苫至佐賀大学, 理工学部, 教授 (40112289) 小倉幸雄佐賀大学, 理工学部, 教授 (00037847) 猿子幸弘佐賀大学, 理工学部, 助教授 (00315178)
Keywords	Mangoldt曲面 / Toponogovの比較定理 / 剛性定理 / Alexandrov空間 / 漸近的等周問題 / 確率過程の弱収束 / Chern-Simons積分 / 作用素の可逆性
Research Abstract	1.完備リーマン多様体のradial curvatureの下限がMangoldt曲面や回転面のガウス曲率で与えられたとき、Alexandrov-Toponogovの比較定理が成立する事を証明した。 2.非コンパクト完備リーマン多様体をradial curvatureの条件下でコンパクト化して、剛性定理が成立する条件を求めた。 3.AlexandrovとZalgallerの比較定理を2次元Alexandrov空間上で証明し、応用として空間のスケーリングにおける収束定理を証明した。 4.2次元Alexandrov空間に対する漸近的等周問題を比較幾何の観点から解決した。 5.正の時刻を固定するとき熱核が上から一様に押さえられるようなコンパクト多様体の列がスペクトル収束するとき、それらから定まる確率過程の列が弱収束することを得た。 6.Chern-Simons積分における3次の項の処理を、積分の正規化と上下積分の償いcompensationのアイデアを用いて行い、摂動型漸近評価を得た。 7.ある種の無限次元単体における作用素が、可逆性を持つ為の1階微分の項の具体形を求め、さらにそのときの付随する2乗可積分空間を特定した。

Research Products

(13 results)

All Other

All Publications (13 results)

[Publications] K.Shiohama: "Sphere Theorems""Handbook of Differential Geometry", eds. F.Dillen and L.Verstraele. Vol.1. 862-903 (2000)
[Publications] K.Shiohama: "Rigidity and sphere theorems for submanifolds II"Kyushu J. Math. 54・1. 103-109 (2000)
[Publications] K.Shiohama: "Comparison theorems for manifolds with radial curvature bounded below""Proceedings of the First Intern. Symp. on Diff. Geom.", Josai Mathematical Monographs. Vol.3. 81-91 (2001)
[Publications] Y.Itokawa: "Maximal diameter theorems for manifolds with restricted Radial curvature""Proc. Fifth Pacific Rim Geometry Conference", Tohoku Mathematical Publications. No.20. 61-68 (2001)
[Publications] Y.Itokawa: "Generalized Toponogov's theorem for manifolds with radial curvature bounded below"Nagoya Mathematical Journal. (To appear). (2001)
[Publications] K.Shiohama: "Compactification and maximal diameter theorem for noncompact ma nifolds with radial curvature bounded below"Math.Z.. (To appear). (2001)
[Publications] K.Shiohama: "A Survey of Complete Manifolds with Bounded Radial Curvature Function""Proc. International Symposium on Differential Geometry--in honor of Professor Su BuChin--", Shanghai. (To appear). (2002)
[Publications] Y.Ogura: "Weak convergence of laws of stochastic processes on Riemannian manifolds"Prob.Theor.Rel.Fields. 119. 529-557 (2001)
[Publications] Y.Ogura: "Set defuzzification and Choquet integral"International Jounal of Uncertainty Fuzziness and Knowledge-Based Systems. 9. 1-12 (2001)
[Publications] Y.Ogura: "Separability of graph convergence of sequences of fuzzy valued random variables"Fuzzy Sets and Systems. 123. 19-27 (2001)
[Publications] Y.Ogura: "Convergence of local type Dirichlet forms to a non-local type one"Ann.Inst.Henry Poincare. (To appear).
[Publications] K.Handa: "Quasi-invariant measures and their characterization by conditional probabilities"Bull.Sci.math. 125. 583-604 (2001)
[Publications] K.Handa: "Quasi-invariance and reversibility in the Fleming-Viot process"Probab.Theory Related Fields. (To appear).

2001 Fiscal Year Annual Research Report

CAT-空間の距離構造に関する研究

Principal Investigator

塩濱 勝博 佐賀大学, 理工学部, 教授 (20016059)

Research Products

[Publications] K.Shiohama: "Sphere Theorems""Handbook of Differential Geometry", eds. F.Dillen and L.Verstraele. Vol.1. 862-903 (2000)

[Publications] K.Shiohama: "Rigidity and sphere theorems for submanifolds II"Kyushu J. Math. 54・1. 103-109 (2000)

[Publications] K.Shiohama: "Comparison theorems for manifolds with radial curvature bounded below""Proceedings of the First Intern. Symp. on Diff. Geom.", Josai Mathematical Monographs. Vol.3. 81-91 (2001)

[Publications] Y.Itokawa: "Maximal diameter theorems for manifolds with restricted Radial curvature""Proc. Fifth Pacific Rim Geometry Conference", Tohoku Mathematical Publications. No.20. 61-68 (2001)

[Publications] Y.Itokawa: "Generalized Toponogov's theorem for manifolds with radial curvature bounded below"Nagoya Mathematical Journal. (To appear). (2001)

[Publications] K.Shiohama: "Compactification and maximal diameter theorem for noncompact ma nifolds with radial curvature bounded below"Math.Z.. (To appear). (2001)

[Publications] K.Shiohama: "A Survey of Complete Manifolds with Bounded Radial Curvature Function""Proc. International Symposium on Differential Geometry--in honor of Professor Su BuChin--", Shanghai. (To appear). (2002)

[Publications] Y.Ogura: "Weak convergence of laws of stochastic processes on Riemannian manifolds"Prob.Theor.Rel.Fields. 119. 529-557 (2001)

[Publications] Y.Ogura: "Set defuzzification and Choquet integral"International Jounal of Uncertainty Fuzziness and Knowledge-Based Systems. 9. 1-12 (2001)

[Publications] Y.Ogura: "Separability of graph convergence of sequences of fuzzy valued random variables"Fuzzy Sets and Systems. 123. 19-27 (2001)

[Publications] Y.Ogura: "Convergence of local type Dirichlet forms to a non-local type one"Ann.Inst.Henry Poincare. (To appear).

[Publications] K.Handa: "Quasi-invariant measures and their characterization by conditional probabilities"Bull.Sci.math. 125. 583-604 (2001)

[Publications] K.Handa: "Quasi-invariance and reversibility in the Fleming-Viot process"Probab.Theory Related Fields. (To appear).

塩濱勝博佐賀大学, 理工学部, 教授 (20016059)