Home » Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem by Stefan P. Ivanov
Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem Stefan P. Ivanov

Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem

Stefan P. Ivanov

Published March 8th 2011
ISBN : 9789814295703
Hardcover
219 pages
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 About the Book 

The aim of this book is to give an account of some important new developments in the study of the Yamabe problem on quaternionic contact manifolds. This book covers the conformally flat case of the quaternionic Heisenberg group or sphere, whereMoreThe aim of this book is to give an account of some important new developments in the study of the Yamabe problem on quaternionic contact manifolds. This book covers the conformally flat case of the quaternionic Heisenberg group or sphere, where complete and detailed proofs are given, together with a chapter on the conformal curvature tensor introduced very recently by the authors. The starting point of the considered problems is the well-known Folland-Stein Sobolev type embedding and its sharp form that is determined based on geometric analysis. This book also sits at the interface of the generalization of these fundamental questions motivated by the Carnot-Caratheodory geometry of quaternionic contact manifolds, which have been recently the focus of extensive research motivated by problems in analysis, geometry, mathematical physics and the applied sciences. Through the beautiful resolution of the Yamabe problem on model quaternionic contact spaces, the book serves as an introduction to this field for graduate students and novice researchers, and as a research monograph suitable for experts as well.