Short-Time Existence Theorem for the CR Torsion Flow

2018/04/18 by Shu-Cheng Chang, Chang, Shu-Cheng, Chin-Tung Wu +1 · 1 citation
Mathematics · Physics and Astronomy · #32G07 #53C21 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:32G07 #msc:53C21

paper · pdf · doi:10.48550/arxiv.1804.06585

30 pages

arxiv created 2018/04/18 · openalex publication_date 2018/04/18 · arxiv updated 2018/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Cited by

• On the CR analogue of Frankel conjecture and a smooth representative of the first Kohn-Rossi cohomology group

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