Unified theory for geometric flows on Hermitian manifolds.
problem Geometric flows on compact Hermitian manifolds.
method Introducing parabolic C-subsolutions for parabolic equations.
result Unified approach for studying geometric flows.
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9 results for “C-subsolutions”
Proves solvability of general inverse σ_k equations with constant coefficients.
problem Solvability of general inverse σ_k equations with constant coefficients.
method Proves existence of unique solution if a C-subsolution exists.
result Confirms analytical conjecture for deformed Hermitian--Yang--Mills equation.
The paper studies equations on almost Hermitian manifolds with estimates and existence results.
problem Solving Monge-Ampère type equations on compact almost Hermitian manifolds.
method Derives a priori estimates and obtains existence results under admissible conditions.
result Existence of solutions under admissible conditions for Monge-Ampère type equations.
The paper confirms the solvability of a complex equation for a 4D manifold.
problem Solvability of a deformed Hermitian--Yang--Mills equation on a 4D Kähler manifold.
method Used eigenvalues and topological constants to prove the existence of a C-subsolution.
result The existence of a C-subsolution implies the solvability of the deformed Hermitian--Yang--Mills equation when the complex dimension is 4 and θ is close to π.
Uniform bounds for complex equations using Monge-Ampère method.
problem Bounding solutions to complex equations.
method Auxiliary Monge-Ampère equation method.
result Uniform bounds remain valid even as background metrics degenerate.
Paper proves solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
problem Existence of solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
method Derive a priori estimates under the existence of an admissible -subsolution; prove existence of solutions under the condition of existence of a supersolution.
result Proves existence of solutions for the deformed Hermitian-Yang-Mills equation.
Study fully nonlinear elliptic equations on compact hyperhermitian manifolds.
problem Solving fully nonlinear elliptic equations on compact hyperhermitian manifolds.
method Adapting Székelyhidi's approach to the hypercomplex setting, proving a priori estimates.
result Proves solvability of quaternionic Hessian and Monge-Ampère equations on compact flat hyperkähler manifolds.
Study estimates for -Hessian equations on closed manifolds.
problem Estimating solutions to -Hessian equations on closed Riemannian manifolds.
method Introducing pseudo-solutions to generalize -subsolution and proving and estimates.
result Proves estimates for general -Hessian equations on closed manifolds under sharp conditions.
New tan-concavity property for Lagrangian phase operators helps in studying dHYM metrics.
problem Lack of concavity in Lagrangian phase operator for dHYM metrics.
method Introduce tangent Lagrangian phase flow (TLPF) on almost calibrated (1,1)-forms.
result TLPF exists for all positive time and converges to dHYM metrics under certain conditions.