On the estimate of the first eigenvalue of a sub-Laplacian on a pseudo-Hermitian 3-manifold

DOI10.2140/pjm.2007.232.269zbMath1152.58026OpenAlexW2027872391MaRDI QIDQ952997

Hung-Lin Chiu, Shu-Cheng Chang

Publication date: 14 November 2008

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2007.232.269

zbMATH Keywords

eigenvaluegradient estimatediametersub-Laplacianpseudo-Hermitian torsionTanaka-Webster curvatureCR Paneitz operatorpseudo-Hermitian manifoldCarnot-cCarathéodory distance

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Other complex differential geometry (53C56) CR structures, CR operators, and generalizations (32V05) Analysis on CR manifolds (32V20)

Related Items (10)

On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold ⋮ 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 ⋮ An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion ⋮ Bounds for the first eigenvalue of the horizontal Laplacian in positively curved sub-Riemannian manifolds ⋮ The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold ⋮ The Li-Yau-Hamilton inequality for Yamabe flow on a closed CR 3-manifold ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD ⋮ The diameter estimate and its application to CR Obata’s Theorem on closed pseudohermitian $(2n+1)$-manifolds

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