Regularity of geodesics in the spaces of convex and plurisubharmonic functions II
Abstract
In this note we continue our investigation of geodesics in the space of convex and plurisubharmonic functions. We show optimal regularity for geodesics joining two smooth strictly convex functions. We also investigate the regularity theory in the $C^{1,\alpha}$ realm. Finally we discuss the regularity of geodesics joining two toric strictly plurisubharmonic functions.
Fields of Study & Subjects
Geometry and complex manifolds
Geometric Analysis and Curvature Flows
Holomorphic and Operator Theory
Publication details
- Journal / source
- Communications in Analysis and Geometry
- Publisher
- International Press of Boston
- Volume
- 34
- Issue
- 2
- Pages
- 395–421
- Publication date
- 1 January 2026
- Language
- EN