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arXiv · 2405.04948

Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations

Per Åhag·Rafał Czyż·Chinh H. Lu·Alexander Rashkovskii
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Abstract

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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Per Åhag, Rafał Czyż, Chinh H. Lu, Alexander Rashkovskii. 2024-05-08. Kiselman Minimum Principle and Rooftop Envelopes in Complex Hessian Equations. https://arxiv.org/abs/2405.04948

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