A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian

DOI10.1016/j.aim.2015.06.008zbMath1319.53032arXiv1308.3403OpenAlexW1870580145WikidataQ125989866 ScholiaQ125989866MaRDI QIDQ2354394

Xiaodong Wang, Duong Ngoc Son, Song-Ying Li

Publication date: 13 July 2015

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.3403

zbMATH Keywords

eigenvaluerigidityCR-manifoldsKohn Laplacianpseudo-Hermitian

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Embeddings of CR manifolds (32V30)

Related Items (13)

An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces ⋮ The holomorphic sectional curvature and “convex” real hypersurfaces in Kähler manifolds ⋮ The Lichnerowicz-Obata theorem for the Kohn Laplacian in three dimensions ⋮ Eigenvalue estimates for 3-Sasaki structures ⋮ Eigenvalues of the Kohn Laplacian and deformations of pseudohermitian structures on CR manifolds ⋮ On the asymptotic expansions of the proper harmonic maps between balls in Bergman metrics ⋮ The sharp upper bounds for the first positive eigenvalue of the Kohn-Laplacian on compact strictly pseudoconvex hypersurfaces ⋮ Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications ⋮ The Webster scalar curvature and sharp upper and lower bounds for the first positive eigenvalue of the Kohn-Laplacian on real hypersurfaces ⋮ 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 ⋮ The Obata first eigenvalue theorem on a seven-dimensional quaternionic contact manifold

Cites Work

• An Obata-type theorem in CR geometry
• Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains
• Rational dependence of smooth and analytic CR mappings on their jets
• Embeddability for 3-dimensional Cauchy-Riemann manifolds and CR Yamabe invariants
• 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
• Embeddability for Three-Dimensional CR-Manifolds
• Calculus on Heisenberg Manifolds. (AM-119)
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