The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold

DOI10.1007/S12220-012-9354-9zbMath1303.53060arXiv1112.0779OpenAlexW2081788664MaRDI QIDQ472032

Dimiter Vassilev, Alexander Petkov, Stefan Ivanov

Publication date: 18 November 2014

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.0779

zbMATH Keywords

Bochner formulasub-Laplacianfirst eigenvalue estimatequaternionic contact

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60)

Related Items (13)

The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven ⋮ Convexity of the entropy of positive solutions to the heat equation on quaternionic contact and CR manifolds ⋮ A Lichnerowicz-type result on a seven-dimensional quaternionic contact manifold ⋮ Eigenvalue estimates for 3-Sasaki structures ⋮ The almost Schur lemma in quaternionic contact geometry ⋮ Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group ⋮ The Bochner-type formula and the first eigenvalue of the sub-Laplacian on a contact Riemannian 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 ⋮ The topology of quaternionic contact manifolds ⋮ A Lichnerowicz estimate for the spectral gap of a sub-Laplacian ⋮ The Obata first eigenvalue theorem on a seven-dimensional quaternionic contact manifold ⋮ The Lichnerowicz-Obata theorem on sub-Riemannian manifolds with transverse symmetries

Cites Work

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• On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold
• Nonnegativity of CR Paneitz operator and its application to the CR Obata's theorem
• Conformal paracontact curvature and the local flatness theorem
• Quaternionic contact structures in dimension 7
• Pseudo-conformal quaternionic \(CR\) structure on \((4n+3)\)-dimensional manifolds
• On the regularity of subelliptic \(p\)-harmonic functions in Carnot groups
• Geometric second derivative estimates in Carnot groups and convexity
• On the estimate of the first eigenvalue of a sub-Laplacian on a pseudo-Hermitian 3-manifold
• Conformal quaternionic contact curvature and the local sphere theorem
• The entropy formulas for the CR heat equation and their applications on pseudohermitian \((2n+1)\)-manifolds
• Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem
• The Yamabe problem on quaternionic contact manifolds
• Gradient bounds for the horizontal \(p\)-Laplacian on a Carnot group and some applications
• The Cayley transform and uniformly bounded representations
• Gradient regularity for elliptic equations in the Heisenberg group
• The Lichnerowicz theorem on CR manifolds
• The sharp lower bound for the first positive eigenvalue of the sublaplacian on a pseudohermitian 3-manifold
• Certain conditions for a Riemannian manifold to be isometric with a sphere
• Quaternionic contact manifolds with a closed fundamental 4-form
• Subelliptic Cordes estimates
• Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds
• The first eigenvalue of a sublaplacian on a pseudohermitian manifold
• Applications of analysis on nilpotent groups to partial differential equations
• Regularity of quasi-linear equations in the Heisenberg group
• The sharp lower bound for the first positive eigenvalue of a sub-Laplacian on a pseudo-Hermitian manifold
• Yang-Mills fields on quaternionic spaces
• The optimal constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group

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