m-subharmonic and m-plurisubharmonic functions -- on two problems of Sadullaev

2020/04/14 by Dinew, Slawomir · 4 citations
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.06444

Abstract

We show that the spaces of A-m-subharmonic and B-m-subharmonic functions differ in sufficently high dimensions. We also prove that the Monge-Ampère type operator \mathcal M_m associated to the space of m-plurisubharmonic functions does not allow an integral comparison principle except in the classical cases m=1 and m=n. These answer in the negative two problems posed by A. Sadullaev.

Cited by

• Singular Gauduchon Conjecture
• Holomorphic p-Contact and s-Symplectic Line Bundles
• m-Pseudo-effectivity and a Monge-Ampère-Type Equation for Forms of Positive Degree
• m-Positivity and Regularisation

Related

• Plurisubharmonic functions with weak singularities
• Remarks on the modulus of continuity of subharmonic functions
• Local growth of pluri-subharmonic functions
• Radó- type theorem for subharmonic and plurisubharmonic functions
• A comparison principle for bounded plurisubharmonic functions on complex varieties in Cⁿ