arXiv research

In this paper, we show that any compact K$ä$hler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a K$ä$hler-Einstein metric of general type. Moreover, we prove that, on a compact symplectic manifold $X$ homotopic to a compact Riemannian manifold with negative sectional curva…

The paper studies Ricci curvature on Kähler-Ricci flow.

Continuity of complex Monge-Ampère potentials on Kähler manifolds.

We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K $\in$ R on the regular set, the cone angle along the stratum of codimension two is smaller than or equal to 2$π$ and its dimension is at most equal to N. This gives…

We obtain a necessary and sufficient condition of existence of a K{ä}hler-Einstein metric on a $G\times G$-equivariant Fano compactification of a complex connected reductive group $G$ in terms of the associated polytope. This condition is not equivalent to the vanishing of the Futaki invariant. The proof relies on the …

We describe and construct here pseudo-Hermitian structures $θ$ without torsion (i.e. with transversal symmetry) whose Webster-Ricci curvature tensor is a constant multiple of the exterior differential $dθ$. We call these structures pseudo-Hermitian Einstein and our result states that they all can be derived locally fro…

Given a convex body $K \subset \mathbb{R}^n$ with the barycenter at the origin we consider the corresponding K{ä}hler-Einstein equation $e^{-Φ} = \det D^2 Φ$. If $K$ is a simplex, then the Ricci tensor of the Hessian metric $D^2 Φ$ is constant and equals $\frac{n-1}{4(n+1)}$. We conjecture that the Ricci tensor of $D^2…

New local method solves Yamabe problems on compact and non-compact manifolds.

Study on GL(2) geometries on complex manifolds, focusing on Kähler-Einstein and Fano manifolds.

Study on compact strong HKT manifolds and their properties.

Compact metrics on Heisenberg manifolds have a specific condition for being relatively compact.

Defined and proved monotonicity of a product on compact Hermitian manifolds.

Geodesic completeness proven for all compact locally symmetric Lorentz manifolds.

Compact theorem on Hamiltonian stationary submanifolds in symplectic manifolds.

Study shows compact Lorentz manifolds can't have closed geodesics.

Paper proves structure for compact Kähler manifolds with pseudo-effective tangent bundles.

Study describes conformal product structures on compact Kähler manifolds.

Paper studies heat flow for VT harmonic maps on compact manifolds.

Eigenvalue problem for Kähler metrics on compact manifolds.

Study on $(λ,λ)$-eigenfunctions on compact manifolds, showing manifold properties and eigenfamily dimensions.

No conformal product structures on compact manifolds with constant curvature.

Compact metric f-K-contact manifolds constructed via specific transformations.

Classifies compact multiplicity free quasi-Hamiltonian manifolds.

Positive mass theorem for non-smooth metrics on flat manifolds with corners.

Study on Einstein manifolds with specific properties.

In this paper, we establish some compactness results of conformally compact Einstein metrics on $4$-dimensional manifolds. Our results were proved under assumptions on the behavior of some local and non-local conformal invariants, on the compactness of the boundary metrics at the conformal infinity, and on the topology…

Compact hyperbolic complex manifolds are rigid under deformation.

Approximates compact and non-compact Sasakian manifolds in spheres.

Compact 3D Cotton-parallel manifolds are always conformally flat.

Proves almost flat spin^c manifolds bound compact manifolds.

New metrics found on non-Kähler Calabi-Yau manifolds.

The study characterizes compact homogeneous manifolds with Bismut parallel torsion.

Study Szegő kernel on non-compact CR manifolds with specific conditions.

In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones SG in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence…

We extend to metric compact mapping tori a splitting result for coKähler manifolds. In particular, we prove that a compact Vaisman manifold is finitely covered by the product of a Sasakian manifold and a circle.

Compact manifolds with specific cover properties are hyperbolic.

We study compact Riemannian manifolds for which the light between any pair of points is blocked by finitely many point shades. Compact flat Riemannian manifolds are known to have this finite blocking property. We conjecture that amongst compact Riemannian manifolds this finite blocking property characterizes the flat m…

Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.

Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms pres…

Study pinched self-dual Weyl curvature in compact 4-manifolds.

In this paper we first use the result in $[12]$ to remove the assumption of the $L^2$ boundedness of Weyl curvature in the gap theorem in $[9]$ and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…

The paper proves conditions for compact complex manifolds to be Kahler outside analytic subsets.

This paper extends 3D results to higher dimensions, proving compactness for PIC1 pinched manifolds.

Sharp lower bound for $p$-Laplacian eigenvalue on non-compact manifolds.

Proves bounded subsolution theorem for complex Monge-Ampère equation on compact Hermitian manifolds.

Method calculates function integrals on complex manifolds.

Study describes global sections of chiral de Rham complex on compact Ricci-flat Kähler manifolds.