An Obata-type theorem in CR geometry

DOI10.4310/JDG/1381931736zbMath1277.32038arXiv1207.4033OpenAlexW2962764038WikidataQ115169124 ScholiaQ115169124MaRDI QIDQ378049

Song-Ying Li, Xiaodong Wang

Publication date: 20 November 2013

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.4033

zbMATH Keywords

sublaplacianCR spherepseudohermitian manifold

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Analysis on CR manifolds (32V20)

Related Items (17)

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 ⋮ The Lichnerowicz-Obata theorem for the Kohn Laplacian in three dimensions ⋮ On the asymptotic expansions of the proper harmonic maps between balls in Bergman metrics ⋮ An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion ⋮ The Bochner-type formula and the first eigenvalue of the sub-Laplacian on a contact Riemannian manifold ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ The sharp upper bounds for the first positive eigenvalue of the Kohn-Laplacian on compact strictly pseudoconvex hypersurfaces ⋮ Uniqueness results on CR manifolds ⋮ Liouville-type theorems for CC-harmonic maps from Riemannian manifolds to pseudo-Hermitian manifolds ⋮ Integral equations on compact CR manifolds ⋮ Lichnerowicz-Obata theorem for Kohn Laplacian on the real ellipsoid ⋮ CR-analogue of the Siu-∂\overline{∂}-formula and applications to the rigidity problem for pseudo-Hermitian harmonic maps ⋮ 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 ⋮ A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian

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