The J-equation and the supercritical deformed Hermitian–Yang–Mills equation
G Chen - Inventiones mathematicae, 2021 - Springer
In this paper, we prove that for any Kähler metrics ω _0 ω 0 and χ χ on M, there exists a
Kähler metric ω _ φ= ω _0+-1 ∂ ̄ ∂ φ> 0 ω φ= ω 0+-1∂∂¯ φ> 0 satisfying the J-equation …
Kähler metric ω _ φ= ω _0+-1 ∂ ̄ ∂ φ> 0 ω φ= ω 0+-1∂∂¯ φ> 0 satisfying the J-equation …
A Nakai–Moishezon type criterion for supercritical deformed Hermitian–Yang–Mills equation
The deformed Hermitian–Yang–Mills equation is a complex Hessian equation on compact
Kähler manifolds that corresponds to the special Lagrangian equation in the context of the …
Kähler manifolds that corresponds to the special Lagrangian equation in the context of the …
A class of curvature type equations
P Guan, X Zhang - arXiv preprint arXiv:1909.03645, 2019 - arxiv.org
In this paper, we study the solvability of a general class of fully nonlinear curvature
equations, which can be viewed as generalizations of the equations for Christoffel …
equations, which can be viewed as generalizations of the equations for Christoffel …
A numerical criterion for generalised Monge-Ampère equations on projective manifolds
VV Datar, VP Pingali - Geometric and Functional Analysis, 2021 - Springer
We prove that generalised Monge-Ampère equations (a family of equations which includes
the inverse Hessian equations like the J-equation, as well as the Monge-Ampère equation) …
the inverse Hessian equations like the J-equation, as well as the Monge-Ampère equation) …
Stability and the deformed Hermitian-Yang-Mills equation
TC Collins, Y Shi - arXiv preprint arXiv:2004.04831, 2020 - arxiv.org
We survey some recent progress on the deformed Hermitian-Yang-Mills (dHYM) equation.
We discuss the role of geometric invariant theory (GIT) in approaching the solvability of the …
We discuss the role of geometric invariant theory (GIT) in approaching the solvability of the …
The deformed Hermitian Yang–Mills equation on three-folds
VP Pingali - Analysis & PDE, 2022 - msp.org
We prove an existence result for the deformed Hermitian Yang–Mills equation for the full
admissible range of the phase parameter, ie, 𝜃^∈(π 2, 3 π 2), on compact complex three …
admissible range of the phase parameter, ie, 𝜃^∈(π 2, 3 π 2), on compact complex three …
Regularity of fully non-linear elliptic equations on Hermitian manifolds. II
R Yuan - arXiv preprint arXiv:2001.09238, 2020 - arxiv.org
In this paper we investigate the regularity and solvability of solutions to Dirichlet problem for
fully non-linear elliptic equations with gradient terms on Hermitian manifolds, which include …
fully non-linear elliptic equations with gradient terms on Hermitian manifolds, which include …
The deformed Hermitian-Yang-Mills equation on the blowup of
A Jacob, N Sheu - arXiv preprint arXiv:2009.00651, 2020 - arxiv.org
We study the deformed Hermitian-Yang-Mills equation on the blowup of complex projective
space. Using symmetry, we express the equation as an ODE which can be solved using …
space. Using symmetry, we express the equation as an ODE which can be solved using …
The Dirichlet problem for the k-Hessian equation on a complex manifold
TC Collins, S Picard - American Journal of Mathematics, 2022 - muse.jhu.edu
We solve the Dirichlet problem for $ k $-Hessian equations on compact complex manifolds
with boundary, given the existence of a subsolution. Our method is based on a second order …
with boundary, given the existence of a subsolution. Our method is based on a second order …
Pseudoconvexity for the special Lagrangian potential equation
FR Harvey, HB Lawson - Calculus of Variations and Partial Differential …, 2021 - Springer
Abstract The Special Lagrangian Potential Equation for a function u on a domain Ω ⊂ R^ n
Ω⊂ R n is given by tr {\arctan (D^ 2\, u)\}= θ tr arctan (D 2 u)= θ for a contant θ ∈ (-n π\over …
Ω⊂ R n is given by tr {\arctan (D^ 2\, u)\}= θ tr arctan (D 2 u)= θ for a contant θ ∈ (-n π\over …