3 citations · 4 across the 7 of their papers we have counts for
8 papers
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…
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.…
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…
Harmonic forms on ALE Ricci-flat 4-manifolds
Gao Chen, Hao Yan
In this paper, we compute the expansion of some harmonic functions and 1-forms on ALE Ricci-flat 4-manifolds.
Lecture notes on generalized Monge-Ampère equations and subvarieties
Gao Chen
These are the lecture notes for the Morningside Center of Mathematics Geometry Summer School on August 15-20, 2022. These lectures sketch the results by Yau, Demailly-Paun, the aut…
Torelli-type theorems for gravitational instantons with quadratic volume growth
Gao Chen, Jeff Viaclovsky, Ruobing Zhang
We prove Torelli-type uniqueness theorems for both ALG gravitational instantons and ALG gravitational instantons which are of order . That is, the periods uniquely character…
Gravitational instantons with quadratic volume growth
Gao Chen, Jeff Viaclovsky
There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG and ALG. Gravitational instantons of type ALG were previousl…
Hodge theory on ALG manifolds
Gao Chen, Jeff Viaclovsky, Ruobing Zhang
We develop a Fredholm Theory for the Hodge Laplacian in weighted spaces on ALG manifolds in dimension four. We then give several applications of this theory. First, we show the…