Quasiconformal Mappings and Analysis: A Collection of Papers Honoring F.W. Gehring

ISBN-13: 9780387982991 / Angielski / Twarda / 1997 / 378 str.

Peter Duren; Peter Duren; Juha Heinonen

Opis

In August 1995 an international symposium on "Quasiconformal Mappings and Analysis" was held in Ann Arbor on the occasion of Professor Fred erick W. Gehring's 70th birthday and his impending retirement from the Mathematics Department at the University of Michigan. The concept of the symposium was to feature broad survey talks on a wide array of topics related to Gehring's basic research contributions in the field of quasicon formal mappings, emphasizing their relations to other parts of analysis. Principal speakers were Kari Astala, Albert Baernstein, Clifford Earle, Pe ter Jones, Irwin Kra, OUi Lehto, Gaven Martin, Dennis Sullivan, and Jussi Vaisala. Financial support was provided by the National Science Founda tion, with additional grants from the University of Michigan and from the Institute for Mathematics and its Applications. The symposium was a great success. The speakers rose to the occasion and presented excellent survey lectures. The present volume was conceived as a means for disseminating those expositions to a wider audience. Ad ditional mathematicians, some of whom had not been able to attend the symposium, were invited to contribute similar articles. The result is a fit ting tribute to Fred Gehring's pre-eminent role in developing the theory of quasiconformal mappings, through his own research and writings and lec tures, and through his supervision of graduate students. The volume begins with descriptions of Gehring's mathematical career and an overview of his research achievements.

Spis treści

F.W. Gehring: A Biographical Sketch.- The Mathematics of F.W. Gehring.- Publications of F.W. Gehring.- Ph.D. Students of F.W. Gehring.- Fred Gehring and Finnish Mathematics.- Planar Quasiconformal Mappings;Deformations and Interactions.- Local Minimality Results Related to the Bloch and Landau Constants.- The Apollonian Metric of a Domain in $$ {\mathbb^n} $$.- Conjugacy Invariants of Möbius Groups.- Extremal Quasiconformal Mappings in Plane Domains.- On the Asymptotic Behavior of Quasiconformal Mappings in Space.- The Gehring Lemma.- Old and New on the Quasihyperbolic Metric.- Kleinian Groups; Eichler Cohomology and the Complex Theory.- On the Geometry of Kleinian Groups.- Old and New on the Schwarzian Derivative.- The Gehring-Hayman Inequality in Conformal Mapping.- Extremal Extensions from the Circle to the Disk.- Construction of Quasiregular Mappings.- Mappings and Spaces.- Questions on Quasiconformal Maps in Space.- List of Contributors.