CR-analogue of the Siu-∂\overline{∂}-formula and applications to the rigidity problem for pseudo-Hermitian harmonic maps

DOI10.1090/proc/12997zbMath1429.32037arXiv1709.09395OpenAlexW2759999162MaRDI QIDQ5238096

Duong Ngoc Son, Song-Ying Li

Publication date: 28 October 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.09395

zbMATH Keywords

Kähler manifoldSiu's \(\partial\overline\partial\)-formulastrictly pseudoconvex pseudo-Hermitian manifold

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Analysis on CR manifolds (32V20) Negative curvature complex manifolds (32Q05)

Related Items (4)

Local Hopf lemma for certain degenerate elliptic operators on the half-space ⋮ On the asymptotic expansions of the proper harmonic maps between balls in Bergman metrics ⋮ Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications ⋮ Rigidity theorem for harmonic maps with complex normal boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• An Obata-type theorem in CR geometry
• An explicit formula for the Webster pseudo-Ricci curvature on real hypersurfaces and its application for characterizing balls in \(\mathbb C^n\)
• Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains
• The complex-analyticity of harmonic maps and the strong rigidity of compact Kaehler manifolds
• Pluriharmonic boundary values
• Pseudo-hermitian structures on a real hypersurface
• Harmonic maps and strictly pseudoconvex CR manifolds.
• On the holomorphicity of proper harmonic maps between unit balls with the Bergman metrics
• Pseudoharmonic maps and vector fields on \(CR\) manifolds
• A new characterization of the CR sphere and the sharp eigenvalue estimate for the Kohn Laplacian
• The Fefferman Metric and Pseudohermitian Invariants
• Applications of harmonic maps to Kähler geometry
• Psuedo-Einstein Structures on CR Manifolds
• Pseudoharmonic maps from nondegenerate CR manifolds to Riemannian manifolds
• Harmonic Mappings of Riemannian Manifolds

This page was built for publication: CR-analogue of the Siu-∂\overline{∂}-formula and applications to the rigidity problem for pseudo-Hermitian harmonic maps