Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
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Publication:983898
DOI10.4171/JEMS/222zbMath1196.53023arXivmath/0703044WikidataQ125599527 ScholiaQ125599527MaRDI QIDQ983898
Dimiter Vassilev, Stefan Ivanov, Ivan Minchev
Publication date: 13 July 2010
Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0703044
Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Sub-Riemannian geometry (53C17)
Related Items (21)
The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven ⋮ A Lichnerowicz-type result on a seven-dimensional quaternionic contact manifold ⋮ Perturbation of Yamabe equation on Iwasawa \(N\) groups in presence of symmetry ⋮ The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group ⋮ Sharp Hardy-Littlewood-Sobolev inequalities on quaternionic Heisenberg groups ⋮ Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group ⋮ The optimal constant in the \(L^2\) Folland-Stein inequality on the H-type group ⋮ Quaternionic Kähler and \(\mathrm{Spin}(7)\) metrics arising from quaternionic contact Einstein structures ⋮ The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold ⋮ A Bonnet-Myers type theorem for quaternionic contact structures ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ Sharp Hardy-Littlewood-Sobolev inequalities on a class of H-type groups ⋮ On the equivalence of quaternionic contact structures ⋮ Conformal quaternionic contact curvature and the local sphere theorem ⋮ The topology of quaternionic contact manifolds ⋮ On the existence of local quaternionic contact geometries ⋮ The qc Yamabe problem on non-spherical quaternionic contact manifolds ⋮ The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of \(F_{4(-20)}\) ⋮ Unnamed Item ⋮ On the tangential Cauchy-Fueter operators on nondegenerate quadratic hypersurfaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb {H}^2}$\end{document} ⋮ The Obata first eigenvalue theorem on a seven-dimensional quaternionic contact manifold
Cites Work
- Unnamed Item
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- Quaternionic contact structures in dimension 7
- Pseudo-conformal quaternionic \(CR\) structure on \((4n+3)\)-dimensional manifolds
- Conformal quaternionic contact curvature and the local sphere theorem
- Existence of solutions and regularity near the characteristic boundary for sub-Laplacian equations on Carnot groups
- The Yamabe problem on quaternionic contact manifolds
- The Yamabe problem on CR manifolds
- Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
- Subelliptic estimates and function spaces on nilpotent Lie groups
- Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups.
- Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
- The conjectures on conformal transformations of Riemannian manifolds
- The Yamabe problem
- 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
- Strong Rigidity of Locally Symmetric Spaces. (AM-78)
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