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A Hermitian Curvature Flow
A Hermitian curvature flow on a compact Calabi-Yau manifold is proposed and a regularity result is obtained. The solution of the flow, if exists, is...
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Notes concerning Codazzi pairs on almost anti-Hermitian manifolds
Let ∇ be a linear connection on a 2 n -dimensional almost anti-Hermitian manifold M equipped with an almost complex structure J , a pseudo-Riemannian...
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Remarks on Some Compact Symplectic Solvmanifolds
We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients M = Γ G of a simply-connected solvable Lie group G ...
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A Simons-type Integral Inequality for Minimal Surfaces with Constant Kähler Angle in Complex Projective Spaces
In this paper, we establish a Simons-type integral inequality for minimal surfaces with constant Kähler angle in complex projective spaces, and we...
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On the Nonexistence of a Holomorphic Isometric Immersion from a One-dimensional Singular Non-CSC Extremal Kähler Metric to ℂPN
Usually we call a one-dimensional singular non-CSC extremal Kähler metric HCMU metric. In this article, we will prove that there does not exist a...
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Remarks on the balanced metric on Hartogs triangles with integral exponent
In this paper we study the balanced metrics on some Hartogs triangles of exponent γ ∈ ℤ + , i.e. equipped with a natural Kähler form with where μ = ( μ 1 ,...
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Maxwell-Einstein Metrics on Completions of Certain C* Bundles
In this paper, we prove that for some completions of certain fiber bundles there is a Maxwell-Einstein metric conformally related to any given Kähler...
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Pluriclosed Manifolds with Constant Holomorphic Sectional Curvature
A long-standing conjecture in complex geometry says that a compact Hermitian manifold with constant holomorphic sectional curvature must be Kähler...
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Locally Conformal Kähler and Hermitian Yang-Mills Metrics
The author shows that if a locally conformal Kähler metric is Hermitian Yang-Mills with respect to itself with Einstein constant c ≤ 0, then it is a...
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The Adiabatic Limit of Fu—Yau Equations
In this paper, we consider the adiabatic limit of Fu—Yau equations on a product of two Calabi—Yau manifolds. We prove that the adiabatic limit of...
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The Second Hessian Type Equation on Almost Hermitian Manifolds
In this paper, we derive the second order estimate to the 2nd Hessian type equation on a compact almost Hermitian manifold.
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The holomorphic d-scalar curvature on almost Hermitian manifolds
In this paper, we study the existence of conformal metrics with constant holomorphic d-scalar curvature and the prescribed holomorphic d-scalar...
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The twisted conical Kähler-Ricci solitons on Fano manifolds
In this paper, we show the relation between the existence of twisted conical Kähler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound...
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On the Lower Boundedness of Modified K-energy
In this paper we prove that the modified K -energy on a Fano manifold X is bounded from below if X admits a special degeneration whose central fiber...
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COMPATIBILITY BETWEEN NON-KÄHLER STRUCTURES ON COMPLEX (NIL)MANIFOLDS
We study the interplay between the following types of special non-Kähler Hermitian metrics on compact complex manifolds ( locally conformally Kähler , k -...
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The Kähler–Ricci Flow on CP2
We give a direct proof of the convergence of the Kähler–Ricci flow on CP2 without assuming the existence of the Kähler–Einstein metric.
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Complete Kähler metrics with positive holomorphic sectional curvatures on certain line bundles (related to a cohomogeneity one point of view on a Yau conjecture)
In this article, we study Kähler metrics on a certain line bundle over some compact Kähler manifolds to find complete Kähler metrics with positive...
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Extremizers of the J Functional with Respect to the d1 Metric
In previous work, Darvas, George and Smith obtained inequalities between the large scale asymptotic of the J functional with respect to the d 1 metric...
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Superminimal surfaces in hyperquadric Q2
We study a superminimal surface M immersed into a hyperquadric Q 2 in several cases classified by two global defined functions τ X and τ Y , which were...