Fully non-linear parabolic equations on compact Hermitian manifolds

2017/11/29 by D. H. Phong, Phong, Duong H., Tat Dat Tô +1 · 4 citations
Mathematics · #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1711.10697

openalex publication_date 2017/11/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

A notion of parabolic C-subsolutions is introduced for parabolic equations, extending the theory of C-subsolutions recently developed by B. Guan and more specifically G. Székelyhidi for elliptic equations. The resulting parabolic theory provides a convenient unified approach for the study of many geometric flows.

Cited by

• Flows of conformally coclosed G₂-structures with dilaton
• A general comparison principle for the pluripotential complex Monge-Ampère flow
• Polar sets for m-subharmonic functions on compact Hermitian manifolds
• The parabolic split-type Monge-Ampere on split tangent bundle surfaces

Related

• Fully non-linear parabolic equations on compact manifolds with a flat hyperkähler metric
• Fully non-linear elliptic equations on compact Hermitian manifolds
• Convergence of a class of fully non-linear parabolic equations on Hermitian manifolds
• Non-linear degenerate parabolic flow equations and a finer differential structure on Wasserstein spaces
• The parabolic flows for complex quotient equations