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Pré-Publication, Document De Travail Année : 2024

Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations

Résumé

We initiate the study of $m$-subharmonic functions with respect to a semipositive $(1,1)$-form in Euclidean domains, providing a significant element in understanding geodesics within the context of complex Hessian equations. Based on the foundational Perron envelope construction, we prove a decomposition of $m$-subharmonic solutions, and a general comparison principle that effectively manages singular Hessian measures. Additionally, we establish a rooftop equality and an analogue of the Kiselman minimum principle, which are crucial ingredients in establishing a criterion for geodesic connectivity among $m$-subharmonic functions, expressed in terms of their asymptotic envelopes.
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Dates et versions

hal-04571852 , version 1 (09-05-2024)

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Per Åhag, Rafał Czyż, Hoang Chinh Lu, Alexander Rashkovskii. Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations. 2024. ⟨hal-04571852⟩
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