arXiv research

For $J$-holomorphic mappings for a strongly pseudo-convex manifold, we prove elliptic regularity by the argument of boots-strapping.

Two new boundary Schwarz lemmas for holomorphic maps established.

The paper proves a Schwarz lemma for weakly Kähler-Finsler manifolds.

Proof of Muir-Suffridge conjecture for convex maps in complex space.

Study geodesics in Kähler metrics for all time.

In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy classes and each homotopy class has the structure of a real projective manifold. When the target manifold is strictly convex, our results imply t…

Study of complex projective manifolds using arithmetic lattices.

Study on semistable points and convexity of gradient maps for group actions.

We prove that every bounded strictly $J$-convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We apply this result to the study of the dynamics of pseudo-holomorphic maps.

We construct and study a natural homeomorphism between the moduli space of polynomial cubic differentials of degree d on the complex plane and the space of projective equivalence classes of oriented convex polygons with d+3 vertices. This map arises from the construction of a complete hyperbolic affine sphere with pres…

Introduces quasi-holomorphic maps and their properties.

Survey of complex analytic methods in minimal surface theory.

Harmonic map flow preserves almost-holomorphic maps without singularities.

The symplectic vortex equations admit a variational description as global minimum of the Yang-Mills-Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$ over a closed Riemann surface $Σ$ and $u: P \rightarrow X$ is an equivariant map …

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.

Holomorphic maps are a special case of Hermitian pluriharmonic maps between almost Hermitian manifolds.

Proves properties of complex algebraic varieties and local systems.

We construct an infinite dimensional real analytic manifold structure for the space of real analytic mappings from a compact manifold to a locally convex manifold. Here a map is real analytic if it extends to a holomorphic map on some neighbourhood of the complexification of its domain. As is well known the constructio…

Study Kähler groups from orbifold compactifications of curve moduli.

Holomorphic maps of degree one are biholomorphic, confirming a partial order.

Study proper holomorphic maps between symmetric domains, proving rigidity and isometric properties.

Holomorphic maps between moduli spaces are shown to be forgetful for large g.

No non-constant holomorphic maps between certain complex manifolds with specific properties.

Formula calculates residues for maps near holomorphic distributions.

In this paper, we study deformations of holomorphic Poisson maps which extend Horikawa's series of papers on deformations of holomorphic maps in the context of holomorphic Poisson deformations. In appendices, we present deformations of Poisson morphisms in the language of functors of Artin rings which is the algebraic …

The study describes the geometry of surfaces and their representations in SL(3,R).

We prove that Kobayashi isometries between strongly convex domains are holomorphic or anti-holomorphic. More precisely, let $n_1, n_2$ be positive integers and let $Ω_i \subset \C^{n_i}, \ i=1,2$, be bounded $C^3$ strongly convex domains. If $φ: (Ω_1, d^K_{Ω_1}) \rightarrow (Ω_2, d^K_{Ω_2})$ is an isometry, i.e. $ d^K_…

The paper proves Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.

Study finite rank bundle over J-Holomorphic map moduli spaces with exponential decay.

Sharp lower bound for curvature in Kähler manifolds.

We initiate the study of the asymptotic topology of groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers (these are called here as holomorphically convex groups). We prove the $H_1$-semistability conjecture of Geoghegan for holomorphically…

H-holomorphic maps are a parameter version of J-holomorphic maps into contact manifolds. They have arisen in efforts to prove the existence of higher--genus holomorphic open book decompositions and efforts to prove the existence of finite energy foliations and the Weinstein conjecture, as well as in folded holomorphic …

Integral inequalities for holomorphic maps prove rigidity and degeneracy theorems.

Local holomorphic maps preserving (p,p) forms are shown to be isometries.

Paper derives formulas for holomorphic maps between Hermitian manifolds and proves related theorems.

We initiate the study of holomorphically convex groups: groups that can be realized as fundamental groups of smooth complex projective varieties with holomorphically convex universal covers. If $G$ is a holomorphically convex group of cohomological dimension two, we show that $G$ is isomorphic to the fundamental group …

The paper establishes Schwarz type lemmas for pseudo-Hermitian manifolds.

The paper proves a factorization theorem for harmonic maps between Riemann surfaces and manifolds.

Proves rigidity of maps between balls with Hölder boundary continuity.

The paper introduces a new energy density function and proves Liouville type theorems for various maps.

The paper classifies holomorphic maps between Riemann surface configuration spaces.

The paper resolves a problem about metric inequivalence and characterizes proper holomorphic maps.

Study Dirac-harmonic maps on Riemann surfaces and their relation to J-holomorphic curves.

Study the asymptotics of holomorphic maps from polydisk to disk.

We study Lie group structures on groups of the form C^\infty(M,K)}, where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra C^\infty(M,k) for which the evaluation map is smooth. We then prove the existen…

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

Isothermic nets created from special maps for smooth surfaces.

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