Core sets in Kähler manifolds

Date

2023-09-15

Author

Göğüş, Nihat Gökhan
Günyüz, Ozan
Yazıcı, Özcan

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The primary objective of this paper is to study core sets in the setting of m-subharmonic functions on the class of (non-compact) Kähler manifolds. Core sets are investigated in different aspects by considering various classes of plurisubharmonic functions. One of the crucial concepts in studying the structure of this kind of sets is the pseudoconcavity. In a more general way, we will have the structure of core defined with respect to the m-subharmonic functions, which we call m-core in our setting, in terms of m-pseudoconcave sets. In the context of m-subharmonic functions, we define m-harmonic functions and show that, in Cn(n≥2) and more generally in any Kähler manifold of dimension at least 2, m-harmonic functions are pluriharmonic functions for m≥2.

Subject Keywords

Core, m-Subharmonic function, Pseudoconcavity, Pseudoconvexity

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85149897905&origin=inward
https://hdl.handle.net/11511/102636

Journal

Journal of Mathematical Analysis and Applications

DOI

https://doi.org/10.1016/j.jmaa.2023.127175

Collections

Department of Mathematics, Article

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Citation Formats

N. G. Göğüş, O. Günyüz, and Ö. Yazıcı, “Core sets in Kähler manifolds,” Journal of Mathematical Analysis and Applications, vol. 525, no. 2, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85149897905&origin=inward.