On piecewise pluriharmonic functions

2012/06/17 by Boris Kazarnovskii, Kazarnovskii, Boris · 1 citation
Mathematics · Physics and Astronomy · #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Nonlinear Waves and Solitons #math.CV

paper · pdf · doi:10.48550/arxiv.1206.3741

Four tipos corrected

openalex publication_date 2012/06/17 · arxiv created 2012/07/16 · arxiv updated 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend some results on piecewise linear functions on \Cⁿ to piecewise pluriharmonic functions on any complex manifold. We construct a ring generated by currents h and dd^ch, where \h\ is a finite set of piecewise pluriharmonic functions. We prove that, with some restrictions on the set \h\, the map \h↦ dd^ch, dd^ch↦0\ can be continued to the derivation on the ring. As a corollary, the current dd^cg₁\wedge...\wedge dd^cg_k depends on the product of piecewise pluriharmonic functions g₁,...,g_k only.

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