arXiv research

The paper proves that Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.

In this paper, we discuss a rigidity property for holomorphic disks in Teichmüller space. In fact, we give a refinement of Tanigawa's rigidity theorem. We will also treat the rigidity property of holomorphic disks for complex manifolds. We observe the rigidity property is valid for bounded strictly pseudoconvex domains…

Proves rigidity of maps between balls with Hölder boundary continuity.

Study proves rigidity of harmonic maps from 2-torus to complex projective space.

Optimizes dimension estimate for holomorphic functions on Kähler manifolds.

Study proper holomorphic maps between specific domains, proving rigidity under certain conditions.

Local rigidity results for Bergman and Kähler Carathéodory metrics on domains.

We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.

We study the singularities of Legendrian subvarieties of contact manifolds in the complex-analytic category and prove two rigidity results. The first one is that Legendrian singularities with reduced tangent cones are contactomorphically biholomorphic to their tangent cones. This result is partly motivated by a problem…

Study generalizes map properties between Hermitian manifolds preserving specific forms.

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.

The paper proves rigidity theorems on holomorphic isometries into homogeneous domains.

The paper proves rigidity properties of holomorphic isometries into homogeneous Kähler manifolds.

Develops tools for studying intersections of elliptic operators, focusing on $J$-holomorphic maps.

Study on holomorphic curves in 6-sphere with boundary conditions.

We study compact complex 3-manifolds admitting holomorphic Riemannian metrics. We prove a uniformization result: up to a finite unramified cover, such a manifold admits a holomorphic Riemannian metric of constant sectionnal curvature.

The paper proves a Schwarz lemma for mappings between specific types of manifolds.

Maps preserving Carathéodory distance between symmetric domains are rigid.

The Fock-Bargmann-Hartogs domain $D_{n,m}(μ)$ ($μ>0$) in $\mathbf{C}^{n+m}$ is defined by the inequality $\|w\|^2<e^{-μ\|z\|^2},$ where $(z,w)\in \mathbf{C}^n\times \mathbf{C}^m$, which is an unbounded non-hyperbolic domain in $\mathbf{C}^{n+m}$. Recently, Yamamori gave an explicit formula for the Bergman kernel of the…

The paper classifies holomorphic maps between Riemann surface configuration spaces.

Study on non-Kähler Calabi-Yau manifolds and their geometric structures.

The paper studies holomorphic curves in a pseudo-Riemannian space and their moduli space.

New 2D complex hyperbolic structures found on sphere orbibundles.

Compact locally conformal Kähler manifolds with constant Chern holomorphic sectional curvature are necessarily Kähler.

The paper proposes conjectures about moduli space rigidity.

Kahler manifolds with specific curvature properties are close to projective spaces.

This paper shows that every totally-geodesic isometry from the unit disk to a finite-dimensional Teichmüller space for the intrinsic Kobayashi metric is either holomorphic or anti-holomorphic; in particular, it is a Teichmüller disk. Additionally, a similar result is proved for a large class of disk-rigid domains, whic…

Study of flows on complex manifolds with holomorphic properties.

New theorems compare Laplacian on Kähler manifolds.

Hua domain, named after Chinese mathematician Loo-Keng Hua, is defined as a domain in $\mathbb{C}^{n}$ fibered over an irreducible bounded symmetric domain $Ω\subset \mathbb{C}^{d}\;(d<n)$ with the fiber over $z\in Ω$ being a $(n-d)$-dimensional generalized complex ellipsoid $Σ(z)$. In general, a Hua domain is a nonhom…

This paper extends Witten's holomorphic Morse inequalities to singular spaces.

The study shows that symplectic Lefschetz fibrations can have infinitely many sections.

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a…

Compact pseudo-Hermitian spaces have rigid holomorphic isometries.

The study proves rigidity for mixed Hodge structures and applies to curve families.

Embeds flag manifolds into classical ones, proving rigidity in Kähler geometry.

In this paper we define strongly projectively flatness of holomorphic maps into the complex Grassmannian manifold, which is a kind of generalization of holomorphic maps into the complex projective space and prove a rigidity of equivariant strongly projectively flat maps of compact simply connected homogeneous Kähler ma…

The paper shows how certain Kähler groups are uniquely determined by their profinite completions.

We discuss holomorphic isometric embeddings of the projective line into quadrics using a generalisation of the theorem of do Carmo--Wallach to provide a description of their moduli spaces up to image and gauge--equivalence. Moreover, we show rigidity of the real standard map from the projective line into quadrics.

We prove the holomorphic rigidity conjecture of Teichmüller space which loosely speaking states that the action of the mapping class group uniquely determines the Teichmüller space as a complex manifold. The method of proof is through harmonic maps. We prove that the singular set of a harmonic map from a smooth $n$-dim…

Computes colored HOMFLYPT invariants using holomorphic curves.

Method constructs rigid associative submanifolds in twisted G2-manifolds.

Maps between certain configuration spaces are rigid and affine equivalent.

Our aim here is to investigate the holomorphic geometric structures on compact complex manifolds which may not be Kähler. We prove that holomorphic geometric structures of affine type on compact Calabi-Yau manifolds with polystable tangent bundle (with respect to some Gauduchon metric on it) are locally homogeneous. In…

Let $M$ and $N$ be two compact complex manifolds. We show that if the tautological line bundle $\mathscr{O}_{T_M^*}(1)$ is not pseudo-effective and $\mathscr{O}_{T_N^*}(1)$ is nef, then there is no non-constant holomorphic map from $M$ to $N$. In particular, we prove that any holomorphic map from a compact complex mani…

In this paper we establish two boundary versions of the Schwarz lemma. The first is for general holomorphic self maps of bounded convex domains with $C^2$ boundary. This appears to be the first boundary Schwarz lemma for general holomorphic self maps that requires no strong pseudoconvexity or finite type assumptions. T…

For compact complex manifolds with vanishing first Chern class that are compact torus principal bundles over Kähler manifolds, we prove that all holomorphic geometric structures on them, of affine type, are locally homogeneous. For a compact simply connected complex manifold in Fujiki class $\mathcal C$, whose dimensio…

We derive some integral inequalities for holomorphic maps between complex manifolds. As applications, some rigidity and degeneracy theorems for holomorphic maps without assuming any pointwise curvature signs for both the domain and target manifolds are proved, in which key roles are played by total integration of the f…