Convergence of a class of fully non-linear parabolic equations on Hermitian manifolds

2021/12/04 by Mathew George, George, Mathew
Mathematics · #35K10 #35K55 #58J35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2112.02432

openalex publication_date 2021/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of fully non-linear parabolic equations on compact Hermitian manifolds involving symmetric functions of partial Laplacians. Under fairly general assumptions, we show the long time existence and convergence of solutions. We also derive a Harnack inequality for the linearized equation which is used in the proof of convergence.

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