Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group

DOI10.2140/apde.2023.16.839zbMath1527.53033arXiv1504.03142OpenAlexW2281377526MaRDI QIDQ6168316

Stefan Ivanov, Dimiter Vassilev, Ivan Minchev

Publication date: 10 July 2023

Published in: Analysis \& PDE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.03142

zbMATH Keywords

constant scalar curvatureYamabe equationquaternionic contact structures3-Sasakian manifolds

Mathematics Subject Classification ID

Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Almost contact and almost symplectic manifolds (53D15) Sub-Riemannian geometry (53C17)

Related Items (3)

On conformal qc geometry, spherical qc manifolds and convex cocompact subgroups of \(\mathrm{Sp}{(n+1,1)}\) ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ A survey on inverse mean curvature flow in ROSSes

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp Hardy-Littlewood-Sobolev inequalities on the octonionic Heisenberg group
• Sharp constants in several inequalities on the Heisenberg group
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold
• The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds
• Quaternionic contact hypersurfaces in hyper-Kähler manifolds
• Quaternionic contact Einstein manifolds
• Quaternionic contact structures in dimension 7
• Sharp Hardy-Littlewood-Sobolev inequalities on quaternionic Heisenberg groups
• Conformal quaternionic contact curvature and the local sphere theorem
• Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
• Existence of solutions and regularity near the characteristic boundary for sub-Laplacian equations on Carnot groups
• The Yamabe problem on quaternionic contact manifolds
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Symmetry and related properties via the maximum principle
• Best constant in Sobolev inequality
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere
• Sobolev, Poincaré, and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality
• The conjectures on conformal transformations of Riemannian manifolds
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven
• Scalar Curvature Functions in a Conformal Class of Metrics and Conformal Transformations
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Yang-Mills fields on quaternionic spaces
• The optimal constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)

This page was built for publication: Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group