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.
Subextension and approximation of m -subharmonic functions with given boundary values
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Maximal subextension of $m$-subharmonic functions
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.