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Tuesday, July 14, 2020 | History

4 edition of Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem found in the catalog.

# Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem

## by Stefan P. Ivanov

Written in English

Subjects:
• Differential Geometry,
• Group theory,
• Contact manifolds

• Edition Notes

Includes bibliographical references (p. 207-216) and index.

Classifications The Physical Object Statement Stefan P. Ivanov, Dimiter N. Vassilev Contributions Vassilev, Dimiter N. LC Classifications QA649 .I89 2011 Pagination xvii, 219 p. ; Number of Pages 219 Open Library OL25102390M ISBN 10 9814295701 ISBN 10 9789814295703 LC Control Number 2011282951 OCLC/WorldCa 496951750

Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, with S. Ivanov and I. Minchev, J. Eur. Math. Soc. (JEMS) 12 (), no. 4, 8. In this paper, we study the CR (Cauchy-Riemann) Yamabe flow with zero CR Yamabe invariant. We use the CR Poincaré inequality and a Gagliardo-Nirenberg type interpolation inequality to show that this flow has the long time solution and the solution converges to a contact form with flat pseudo-Hermitian scalar curvature exponentially.

Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, with St. Ivanov and I. Minchev, MPIM, A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given.   Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem Authors: David Jerison and John M. Lee Journal: J. Amer. Math. Soc. 1 (),

[JL] D. Jerison, J. Lee, Extremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem, J. AMS 1(1), (), 1 - Web of Science Google Scholar [KS] , Y. Sakai, The inverse mean curvature flow in rank one symmetric spaces of non-compact type, Kyushu J. Math. 69 (), - Web of Science Google Scholar. "Conformal quaternionic contact curvature and the local sphere theorem"(with Dimiter Vassilev), Journal de Mathe’matiques Pures et Applique’es, 93 (), pp. IF - , цитирания -

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### Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem by Stefan P. Ivanov Download PDF EPUB FB2

Buy Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem on FREE SHIPPING on qualified orders Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem: Stefan P Ivanov: : BooksCited by:   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.

Sample Chapter(s) Chapter 1: Variational problems related to Sobolev inequalitieson Carnot groups ( KB). Request PDF | Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem | The aim of this book is to give an account of some important new developments in the study of the.

Extremals for the Sobolev inequality on the quaternionic Heisenberg group and the quaternionic contact Yamabe problem. Stefan Ivanov. based on- joint works with Ivan Minchev & Dimiter Vassilev, and arXiv - joint with Dimiter Vassilev, Hamburg, July (Institute) 1 / Abstract.

A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given.

Extremals for the Sobolev inequality on the seven dimensional Hesenberg group are explicitly described and the best constant in the L 2 Folland-Stein embedding theorem is determined.

Abstract. A complete solution to the quaternionic contact Yamabe problem on the seven dimen-sional sphere is given. Extremals for the Sobolev inequality on the seven dimensional Heisenberg group are explicitly described and the best constant in the L2 Folland-Stein embedding theorem is determined.

Title: Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem.

Authors: Stefan Ivanov, Ivan Minchev, Dimiter Vassilev (Submitted on 1 Marlast revised 30 Jul (this version, v3)). Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem. A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given.

Extremals for the Sobolev inequality on the seven dimensional Hesenberg group are explicitly described and the best constant in the $L^2$ Folland-Stein embedding theorem. A complete solution to the quaternionic contact Yamabe problem on the seven dimen- sional sphere is given.

Extremals for the Sobolev inequality on the seven dimensional Heisenberg group are explicitly described and the best constant in the L2Folland-Stein embedding theorem is determined.

Contents 1. Introduction 1 2. In fact, when $$s=0$$ and $$\gamma =0$$, this is the setting of the critical case in the classical Sobolev inequalities, which started this whole line of inquiry, due to its connection with the Yamabe problem on compact Riemannian manifolds [2, 43].

Gives an account of some important 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.

Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem. Journal of the European Mathematical Society, 12 (4), doi/JEMS/ Stefan Ivanov, Ivan Minchev, and Dimiter Vassilev, Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, J.

Eur. Math. Soc. (JEMS) 12 (), no. 4, – MR/JEMS/   D. Jerison, J. LeeExtremals for the Sobolev inequality on the Heisenberg group and the CR Yamabe problem J. Amer. Math. Soc., 1 (1) (), pp. Google Scholar. Solution of the qc Yamabe equation on a 3-Sasakian manifold and extremals of the Sobolev-Folland-Stein inequality on the quaternionic Heisenberg groups Stefan Ivanov XIX Geometricl Seminar, Zlatibor based on joint works with Ivan Minchev, Alexander Petkov & Dimiter Vassilev.

Extremals For The Sobolev Inequality And The Quaternionic Contact Yamabe Problem. [Ivanov Stefan P Et Al.] -- 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.

Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, (with I. Minchev and D. Vassilev), J. Eur. Math. Soc. (JEMS) 12 (), – Abstract. Abstract. A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given.

Extremals for the Sobolev inequality on the seven dimensional Hesenberg group are explicitly described and the best constant in the L 2 Folland-Stein embedding theorem is determined. A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension 4n+ 3 as well as on the quaternionic Heisenberg group is given.

A uniqueness theorem for the qc Yamabe problem in a compact locally 3-Sasakian manifold is shown and the extremals of the Sobolev-Folland-Stein inequality on the quaternionoic Heisenberg. - Extremals for the Sobolev inequality on the seven dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem, (with I.

Minchev and D. Vassilev), J. Eur. Math. Soc. (JEMS) 12 (), –. 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.We review several sharp Hardy-Littlewood-Sobolev-type inequalities (HLS) on I-type groups (rank one), which is a special class of H-type groups, using the symmetrization-free method of Frank and Lieb, who proved the sharp HLS on the Heisenberg group in a seminal paper [FL12b].

We give the sharp HLS both on the compact and noncompact pictures.A partial solution of the quaternionic contact Yamabe problem on the quaternionic sphere is given.

It is shown that the torsion of the Biquard connection vanishes exactly when the trace-free part of the horizontal Ricci tensor of the Biquard connection is zero and this occurs precisely on 3-Sasakian manifolds.

All conformal transformations sending the standard flat torsion-free quaternionic.