Short-Time Existence Theorem for the CR Torsion Flow

Abstract

In this paper, we study the torsion flow which is served as the CR analogue of the Ricci flow in a closed pseudohermitian manifold. We show that there exists a unique smooth solution to the CR torsion flow in a small time interval with the CR pluriharmonic function as an initial data. In spirit, it is the CR analogue of the Cauchy-Kovalevskaya local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems