2021/08/06 by Bo Guan, Guan, Bo, Xiaolan Nie +1 · 1 citation
Mathematics · #35J15 #35J60 #53C21 #53C55 #58J05 #A priori and a posteriori #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Applied mathematics #Class (philosophy) #Computer science #Conjecture #Cover (algebra) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hermitian matrix #Mathematical analysis #Mathematics #Nonlinear system #Order (exchange) #Physics #Pure mathematics #Work (physics) #math.AP #math.DG #msc:35J15 #msc:35J60 #msc:53C21 #msc:53C55 #msc:58J05
paper · pdf · doi:10.48550/arxiv.2108.03308
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/08/06 · openalex publication_date 2021/08/06 · arxiv updated 2021/08/10 · openalex created_date 2021/08/16 · openalex updated_date 2026/07/28
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a conjecture by Gauduchon which extends the Calabi conjecture; this was one of the original motivations to this work. We were also motivated by the fact that there had been increasing interests in fully nonlinear pde's from complex geometry in recent years, and aimed to develop general methods to cover as wide a class of equations as possible.