Complex differential geometry and nonlinear differential equations
About this Title
Yum Tong Siu, Editor
Publication: Contemporary Mathematics
Publication Year : Volume 49
ISBNs: 978-0-8218-5049-7 (print); 978-0-8218-7634-3 (online)
MathSciNet review: 833798
This collection of survey articles and research papers focuses on some of the most fruitful methods and ideas in the recently very active field of complex differential geometry and nonlinear differential equations. The topics found in this 1984 Summer Research Conference Proceedings include the local embedding of Cauchy-Riemann structures, minimal varieties, harmonic maps, Chern number inequalities for singular Kähler surfaces, the spectrum of the Laplacian for Kähler manifolds, foliations, vanishing theorems, and complex Finsler metrics.
Papers of particular note include Mok's survey on foliation techniques and vanishing theorems, a succinct account of one of the most important methods in several complex variables which has recently produced some very good results, and the research articles by Cheng-Yau and Sampson, which contain highly significant new results.
Both researchers and graduate students in the fields of several complex variables, differential geometry, and partial differential equations will find this material especially useful.
Table of Contents
- Takao Akahori – The new approach to the local embedding theorem of CR-structures for (the local solvability for the operator in the abstract sense) [MR 833799]
- Michael T. Anderson – Remarks on curvature integrals and minimal varieties [MR 833800]
- J. Bland, T. Duchamp and M. Kalka – On the automorphism group of strictly convex domains in [MR 833801]
- S. Y. Cheng and S.-T. Yau – Inequality between Chern numbers of singular Kähler surfaces and characterization of orbit space of discrete group of [MR 833802]
- Jozef Dodziuk – Laplacian on manifolds and analogous difference operator for graphs [MR 833803]
- J. F. Glazebrook – On isotropic harmonic maps to real and quaternionic Grassmannians [MR 833804]
- S. I. Goldberg – Characterizing by the spectrum of the Laplacian [MR 833805]
- Mario J. Micallef – Stable minimal surfaces in flat tori [MR 833806]
- Ngaiming Mok – Foliation techniques and vanishing theorems [MR 833807]
- H. L. Royden – Complex Finsler metrics [MR 833808]
- J. H. Sampson – Applications of harmonic maps to Kähler geometry [MR 833809]
- S. M. Webster – On the relation between Chern and Pontrjagin numbers [MR 833810]
- J. C. Wood – Harmonic morphisms, foliations and Gauss maps [MR 833811]