## Journal of Differential Geometry

### Calabi-Yau theorem and Hodge-Laplacian heat equation ina closed strictly pseudoconvex CR manifold

#### Abstract

In this paper, we address the Calabi-Lee conjecture for pseudo-Einstein contact structure via the CR Poincaré-Lelong equation. Then we confirm the Calabi-Yau Theorem via Hodge-Laplacian heat flow in a closed strictly pseudoconvex CR $(2n + 1)$-manifold $(M , \theta)$ for $n \geq 2$. With its applications, we affirm a partial answer of the CR Frankel conjecture in a closed spherical strictly pseudoconvex CR $(2n + 1)$-manifold.

#### Article information

Source
J. Differential Geom., Volume 97, Number 3 (2014), 395-425.

Dates
First available in Project Euclid: 22 July 2014

https://projecteuclid.org/euclid.jdg/1406033975

Digital Object Identifier
doi:10.4310/jdg/1406033975

Mathematical Reviews number (MathSciNet)
MR3263510

Zentralblatt MATH identifier
1295.42003

#### Citation

Chang, Der-Chen; Chang, Shu-Cheng; Tie, Jingzhi. Calabi-Yau theorem and Hodge-Laplacian heat equation ina closed strictly pseudoconvex CR manifold. J. Differential Geom. 97 (2014), no. 3, 395--425. doi:10.4310/jdg/1406033975. https://projecteuclid.org/euclid.jdg/1406033975

#### Corrections

• Authors' corrections: Der-Chen Chang, Shu-Cheng Chang, Jingzhi Tie. Erratum to “Calabi–Yau theorem and Hodge–Laplacian heat equation in a closed strictly pseudoconvex CR $(2n + 1)$-manifold”. J. Differential Geom. Volume 102, Number 2, 2016, page 351.