Recent Topics in Differential and Analytic Geometry, Volume 18

Part I

[A] Topics in Complex Differential Geometry

Introduction

Lecture I Harmonic Mappings and Holomorphic Foliations

Lecture II Uniformization of Compact Kähler Manifolds of Nonnegative Curvature

Lecture III Compactification of Complete Kähler Manifolds of Positive Curvature

Lecture IV Compactification of Complete Kähler-Einstein Manifolds of Finite Volume

[B] Collapsing of Riemannian Metrics

Hausdorff Convergence of Riemannian Manifolds and Its Applications

Part II

(1) Compact Kähler Manifolds with Parallel Ricci Tensor

(2) Eta Invariants and Automorphisms of Compact Complex Manifolds

(3) Poincaré Bundle and Chern Classes

(4) Harmonic Functions with Growth Conditions on a Manifold of Asymptotically Nonnegative Curvature II

(5) Homogeneous Einstein Metrics on Certain Kähler C-Spaces

(6) An Application of Kähler-Einstein Metrics to Singularities of Plane Curves

(7) On Rotationally Symmetric Hamilton's Equation for Kähler-Einstein Metrics

(8) An Algebraic Character Associated with Poisson Brackets

(9) Compactification of the Moduli Space of Einstein-Kähler Orbifolds

(10) Self-Duality of ALE Ricci Flat 4-Manifolds and Positive Mass Theorem

(11) Compactification of Moduli Spaces of Einstein-Hermitian Connections for Null-Correlation Bundles

(12) Einstein-Kähler Metrics on Minimal Varieties of General Type and an Inequality between Chern Numbers

Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains.

Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind.

This book is a valuable resource for graduate students and pure mathematicians.