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The smoothing of $m$-subharmonic functions

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arxiv 1312.1906 v2 pith:3H6NP5FL submitted 2013-12-06 math.CV math.AP

Szymon Pliś This is my paper · ORCID
classification math.CVmath.AP
keywords subharmoniccomplexdomainsequationexistencefunctionfunctionshessian
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abstract

We prove Richberg type theorem for $m$-subharmonic function. The main tool is the complex Hessian equation for which we obtain the existence of the unique smooth solution in strictly pseudoconvex domains.

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Cited by 2 Pith papers

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  1. Complex Hessian equations with prescribed singularity on compact K\"ahler manifolds

    math.CV 2019-09 conditional novelty 7.0 of 10

    The total Hessian mass is monotone in singularity type, and Hessian equations H_m(u)=µ have unique solutions in prescribed singularity classes on compact Kähler manifolds.

  2. Maximal subextension of $m$-subharmonic functions

    math.CV 2026-07 conditional novelty 5.0 of 10

    Finite-weighted-energy m-subharmonic functions on a quasi-m-hyperconvex domain in a compact Kähler manifold extend maximally to the whole manifold with controlled complex Hessian measure and weighted energy.

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