C^1,1 regularity of geodesics in the space of volume forms

2018/06/08 by Jianchun Chu, Chu, Jianchun
Mathematics · Physics and Astronomy · #35J60 #35J70 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary: 58E10 #Secondary: 58D17 #math.AP #math.DG #msc:35J60 #msc:35J70 #msc:58D17 #msc:58E10

paper · pdf · doi:10.48550/arxiv.1806.03065

7 pages; v2 some more details added, typos corrected

openalex publication_date 2018/06/08 · arxiv created 2018/07/02 · arxiv updated 2018/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a C^1,1 estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the C^1,1 regularity of geodesics in the space of volume forms.

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