Geometry and Analysis on Manifolds: In Memory of Professor Shoshichi Kobayashi (Progress in Mathematics Book 308)

This Volume Is Dedicated To The Memory Of Shoshichi Kobayashi, And Gathers Contributions From Distinguished Researchers Working On Topics Close To His Research Areas. The Book Is Organized Into Three Parts, With The First Part Presenting An Overview Of Professor Shoshichi Kobayashi's Career. This Is Followed By Two Expository Course Lectures (the Second Part) On Recent Topics In Extremal Kähler Metrics And Value Distribution Theory, Which Will Be Helpful For Graduate Students In Mathematics Interested In New Topics In Complex Geometry And Complex Analysis. Lastly, The Third Part Of The Volume Collects Authoritative Research Papers On Differential Geometry And Complex Analysis. Professor Shoshichi Kobayashi Was A Recognized International Leader In The Areas Of Differential And Complex Geometry. He Contributed Crucial Ideas That Are Still Considered Fundamental In These Fields. The Book Will Be Of Interest To Researchers In The Fields Of Differential Geometry, Complex Geometry, And Several Complex Variables Geometry, As Well As To Graduate Students In Mathematics. --provided By Publisher. Part 1: About Shoshichi Kobayashi -- Part 2: Algebraic Geometry And Complex Analysis -- Part 3: Differential Geometry. Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, Alan Weinstein, Editors. Includes Bibliographical References. Front Matter....Pages i-viii Front Matter....Pages 1-1 In Memory of Professor Shoshichi Kobayashi....Pages 3-12 Events Surrounding the Birth of the Kobayashi Metric....Pages 13-15 Academic Genealogy of Shoshichi Kobayashi and Individuals Who Influenced Him....Pages 17-38 Front Matter....Pages 39-39 Algebraic Differential Equations for Entire Holomorphic Curves in Projective Hypersurfaces of General Type: Optimal Lower Degree Bound....Pages 41-142 Kobayashi Hyperbolicity and Lang’s Conjecture....Pages 143-151 A Lemma on Hartogs Function and Application to Levi Flat Hypersurfaces in Hopf Surfaces....Pages 153-157 On the Extremal Measure on a Complex Manifold....Pages 159-175 A Lang Exceptional Set for Integral Points....Pages 177-207 Kobayashi Hyperbolicity and Higher-dimensional Nevanlinna Theory....Pages 209-273 Geometry and Arithmetic on the Siegel–Jacobi Space....Pages 275-325 On the Pseudonorm Project of Birational Classification of Algebraic Varieties....Pages 327-339 Front Matter....Pages 341-341 The Weighted Laplacians on Real and Complex Metric Measure Spaces....Pages 343-351 Locally Conformally Kähler Structures on Homogeneous Spaces....Pages 353-372 A Note on Vanishing Theorems....Pages 373-382 Dupin Hypersurfaces in Lie Sphere Geometry....Pages 383-394 The Donaldson–Futaki Invariant for Sequences of Test Configurations....Pages 395-403 Strong K-stability and Asymptotic Chow-stability....Pages 405-411 Traces and Characteristic Classes in Infinite Dimensions....Pages 413-435 Moment Map Description of the Cartan–Münzner Polynomials of Degree Four....Pages 437-447 Ribaucour Pairs Corresponding to Dual Pairs of Conformally Flat Hypersurfaces....Pages 449-469 Front Matter....Pages 341-341 Geometry of Symmetric R -spaces....Pages 471-481