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math.DG2026
Geodesics for generalised Monge-Ampère equations
Gao Chen, Kartick Ghosh, Sijie Nie
Xiuxiong Chen proved the existence of geodesics in the space of Kähler potentials and the convexity of the -functional along geodesics. Analogous…
math.DG2026
A numerical criterion for complex Hessian type equations on projective manifolds
Gao Chen, Sijie Nie, Yulun Xu
We prove a Nakai-Moishezon-type criterion for complex Hessian-type equations on projective manifolds whose associated degree- polynomials are strongly strictly right-Noetherian.…
math.DG2026
On The Ellipticity of Generalised Monge-Ampère Equations on Vector Bundles
Gao Chen, Kartick Ghosh
In this paper, we study the ellipticity of the vector bundle versions of the Monge-Ampère, , dHYM and -equations at a point. These are nonlinear geometric partial differe…