Generalized Monge-Ampère-type equations on holomorphic vector bundles over compact Kähler manifolds fail to preserve ellipticity along continuity paths when dimension and rank are at least three, except for the σ₂ case which succeeds.
Ballal and Vamsi P
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On The Ellipticity of Generalised Monge-Amp\`ere Equations on Vector Bundles
Generalized Monge-Ampère-type equations on holomorphic vector bundles over compact Kähler manifolds fail to preserve ellipticity along continuity paths when dimension and rank are at least three, except for the σ₂ case which succeeds.