نقشه‌های هارمونیک و هندسه دیفرانسیل: جشنواره‌ای از نقشه‌های هارمونیک به افتخار شصتمین سالگرد جان سی. وود، ۷-۱۰ سپتامبر ۲۰۰۹ کالیاری، ایتالیا (ریاضیات معاصر)

This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces Contents 6 Preface 8 List of Participants 10 Thirty-nine Years of Harmonic Maps 12 Constant Mean Curvature Surfaces: An Integrable Systems Perspective 18 Explicit Constructions of Harmonic Maps 52 Discrete Harmonic Map Heat Flow on a Finite Graph 86 Contact Pairs and Locally Conformally Symplectic Structures 96 Congruence Curves of the Goldstein-Petrich Flows 110 Differential Geometry of Lagrangian Submanifolds and Hamiltonian Variational Problems 126 A Report on Locally Conformally Kähler Manifolds 146 1. Locally conformally Kähler manifolds 146 1.1. Examples 148 1.1.1. Diagonal Hopf manifolds 148 1.1.2. Compact complex surfaces 149 1.1.3. Oeljeklaus-Toma manifolds 149 2. Locally conformally Kähler manifolds with potential 150 2.1. Vaisman manifolds 152 3. Transformation groups of LCK manifolds 156 References 159 k−Hessian Differential Inequalities and the Compact Support Principle 162 The Geometry of Biharmonic Maps 170 Constructing Metrics with Prescribed Geometry 188 On the Regularity of the Space of Harmonic 2-spheresin the 4-sphere 198 Conformal Fibrations of S3 by Circles 206 Harmonic Map Methods for Willmore Surfaces 214 Some Remarks on Invariant Surfaces and Their Extrinsic Curvature 224 Harmonic and Biharmonic Maps from Surfaces 234 Non-divergence Harmonic Maps 242 A Note on Higher-charge Configurations for the Faddeev-Hopf Model 250 A Survey on the DDVV Conjecture 258 On the Characteristic Foliations of Metric Contact Pairs 266 A Note on η-Einstein Manifolds 272 Minimal and Flat Surfaces in H2 × R with Canonical Coordinates 278 Ricci Curvature Properties and Stability on 3-dimensional Kenmotsu Manifolds 284 On the Existence of Harmonic Morphisms from Three-dimensional Lie Groups 290 This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7–10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kähler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.