Estimates for k-Hessian operator and some applications

Wan, Dongrui

doi:10.1007/s10587-013-0037-x

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2015

2022

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Cited by 6 publications

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“…The real Hessian equations have been studied in many papers, both in suitable domains of R n , and on Riemann manifolds, for example in [7,8,18,20,[30][31][32][33][34] to mention only a few. We refer to [35] for state-of-the-art survey of the real Hessian equation theory.…”

Section: Introductionmentioning

confidence: 99%

Complex Hessian Operator and Lelong Number for Unbounded m-subharmonic Functions

Wan

Wang

2015

Potential Anal

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m-subharmonic functions are the right class of admissible solutions to the complex Hessian equation. In this paper, we generalize the definition of the complex Hessian operator to some unbounded m-subharmonic functions, and we prove that the complex Hessian operator is continuous on the monotonically decreasing sequences of m-subharmonic functions. Moreover we establish the Lelong-Jensen type formula and introduce the Lelong number for m-subharmonic functions. A useful inequality for the mixed Hessian operator is showed.

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