Regularity of geodesics in the spaces of convex and plurisubharmonic\n functions

2019/06/04 by Soufian Abja, Sławomir Dinew, Abja, Soufian +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1906.01386

openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we investigate the regularity of geodesics in the space of\nconvex and plurisubharmonic functions. In the real setting we prove (optimal)\nlocal C^1,1 regularity. We construct examples which prove that the global\nC^1,1 regularity fails both in the real and complex case in contrast to the\nK "ahler manifold setting. Finally we show a necessary and sufficient\nconditions for existence of a smooth geodesic between two smooth strictly\nconvex functions.\n

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