Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian Manifolds

TL;DR

This paper proves the existence of nonconstant CR-holomorphic functions with polynomial growth on certain Sasakian manifolds, advancing the understanding of their complex structure and contributing to the CR Yau uniformization conjecture.

Contribution

It establishes the existence of polynomial growth CR-holomorphic functions on Sasakian manifolds with nonnegative pseudohermitian bisectional curvature, a key step toward the CR Yau uniformization conjecture.

Findings

Existence of nonconstant CR-holomorphic functions of polynomial growth

Supports the CR analogue of Yau's uniformization conjecture

Advances understanding of CR geometry on Sasakian manifolds

Abstract

In this paper, we show that there exists a nonconstant CR holomorphic function of polynomial growth in a complete noncompact Sasakian manifold of nonnegative pseudohermitian bisectional curvature with the CR maximal volume growth property. This is the very first step toward the CR analogue of Yau uniformization conjecture which states that any complete noncompact Sasakian manifold of positive pseudohermitian bisectional curvature is CR biholomorphic to the standard Heisenberg group.