Related papers: Complex Plateau problem in non K\"ahler manifolds

We give an equivalent definition of compact locally conformally hyperk\"ahler manifolds in terms of the existence of a nondegenerate complex two-form with natural properties. This is a conformal analogue of Beauville's theorem stating that…

In this work, we extend K. Kodaira's embedding theorem to non compact hermitian complex manifolds and laminations by complex manifolds.

Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kaehler manifolds are considered. Some necessary and sufficient conditions the investigated manifolds be isotropic…

In this expository paper (Bourbaki talk) we survey results of Claire Voisin showing that there exist compact Kaehler manifolds which are not homeomorphic to any projective manifold.

We study the pseudohermitian sectional curvature of a CR manifold.

We introduce the notion of a special complex manifold: a complex manifold (M,J) with a flat torsionfree connection \nabla such that (\nabla J) is symmetric. A special symplectic manifold is then defined as a special complex manifold…

We initiate the study of an analogue of the Yamabe problem for complex manifolds. More precisely, fixed a conformal Hermitian structure on a compact complex manifold, we are concerned in the existence of metrics with constant Chern scalar…

Building on work of Du, Gao, and Yau, we give a characterization of smooth solutions, up to normalization, of the complex Plateau problem for strongly pseudoconvex Calabi--Yau CR manifolds of dimension $2n-1 \ge 5$ and in the hypersurface…

A well known conjecture in complex geometry states that a compact Hermitian manifold with constant holomorphic sectional curvature must be K\"ahler if the constant is non-zero and must be Chern flat if the constant is zero. The conjecture…

We analyze degenerate homogeneous structures of linear type in the pseudo-K\"ahler and para-K\"ahler cases. The local form and the holonomy of pseudo-K\"ahler or para-K\"ahler manifolds admitting such structure are obtained. In addition the…

A Hermitian-symplectic metric is a Hermitian metric whose K\"ahler form is given by the $(1,1)$-part of a closed $2$-form. Streets-Tian Conjecture states that a compact complex manifold admitting a Hermitian-symplectic metric must be…

We apply the parabolic flow method to solving complex quotient equations on closed K\"ahler manifolds. We study the parabolic equation and prove the convergence. As a result, we solve the complex quotient equations.

The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…

Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact…

We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also…

In this paper, we study a slant submanifold of a complex space form. We also obtain an integral formula of Simons' type for a Kaehlerian slant submanifold in a complex space form and apply it to prove our main result.

In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from CR manifolds into Riemannian manifolds or Kahler manifolds. Some basicity, pluriharmonicity and Siu-Sampson type results are established for both…

We study Lie algebras endowed with an abelian complex structure which admit a symplectic form compatible with the complex structure. We prove that each of those Lie algebras is completely determined by a pair (U,H) where U is a complex…

This survey explores a range of classical findings and recent developments related to our understanding of astheno-K\"ahler manifolds. Furthermore, we provide various examples of astheno-K\"ahler manifolds and analyze the challenges…

In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a…