Ivanov, Vissilev: Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem

by Stefan P Ivanov (University of Sofia “St Kliment Ohridski”, Bulgaria) and Dimiter N Vassilev (The University of New Mexico, USA)

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, 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.


  • Quaternionic Contact Structures
  • Sobolev Type Inequalities
  • The Yamabe Problem on a Quaternionic Contact Manifold
  • The Extremals on the Seven Dimensional Heisenberg Group
  • The Conformal Tensor
  • Notes

Readership: Graduate students and research mathematicians interested in differential geometry, global analysis, Yamabe type problems and 3-Sasakian structures.

200 pp. (approx.)
Pub. date: Mar 2011
ISBN: 978-981-4295-70-3, 981-4295-70-1
Price: US$ 79 / £ 54



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