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arXiv · 1909.02936

Schwarz type lemmas for pseudo-Hermitian manifolds

Yuxin Dong·Yibin Ren·Weike Yu
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Abstract

In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the \emph{CR} maps and the transversally holomorphic maps. In terms of some sub-Laplacian or Hessian type Bochner formulas, and comparison theorems in the pseudo-Hermitian version, we are able to establish several Schwarz type results for both the \emph{CR} maps and the transversally holomorphic maps between pseudo-Hermitian manifolds. Finally, we also discuss the \emph{CR} hyperbolicity problem for pseudo-Hermitian manifolds.

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Yuxin Dong, Yibin Ren, Weike Yu. 2019-09-06. Schwarz type lemmas for pseudo-Hermitian manifolds. https://arxiv.org/abs/1909.02936

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