D. Huynh

activity

20152026

most citedConstruction of hyperbolic hypersurfaces of low degree in

p^{n} (c)

6 citations · 15 across the 18 of their papers we have counts for

collaborators

21 papers

math.CV2026

A curvature estimate for holomophic maps on open Riemann surfaces

Yunling Chen, Dinh Tuan Huynh

We apply the technique of jet differentials to establish a Gauss curvature estimate for an open Riemann surface $M$ , equipped with a conformal metric induced from a nonconstant hol…

math.CV2026

Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two

Lei Hou, Dinh Tuan Huynh, Joël Merker +1

This paper establishes new degree bounds for Kobayashi hyperbolicity in dimension two. Our main results are: -- A very generic surface in $P^{3}$ of degree at least $17$ is…

math.CV2025

A Second Main Theorem for Entire Curves Intersecting Three Conics

Lei Hou, Dinh Tuan Huynh, Joël Merker +1

We establish a Second Main Theorem for algebraically nondegenerate entire holomorphic curves $ f: \mathbb{C} \to \mathbb{P}^2 $ intersecting a generic configuration of three coni…

math.CO2024

Some line and conic arrangements and their Waldschmidt constants

Dinh Tuan Huynh, Tran N. K. Linh, Le Ngoc Long

We study the Waldschmidt constant of some configurations in the projective plane. In the first part, we show that the Waldschmidt constant of a set $X$ of $n$ points where…

math.CV2024

Some variants of the generalized Borel Theorem and applications

Dinh Tuan Huynh

In the first part of this paper, we establish some results around generalized Borel's Theorem. As an application, in the second part, we construct example of smooth surface of degr…

math.CV2024

A $p$ -adic Second Main Theorem

Dinh Tuan Huynh

Let $K$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $∣ ∣$ . We establish a Second Main Theorem…

math.CV2024

Degeneracy of holomorphic mappings into or avoiding Fermat type hypersurfaces

Dinh Tuan Huynh

We prove that if $f : C^{p} \to P^{n} (C)$ is a holomorphic mapping of maximal rank whose image lies in the Fermat hypersurface of degree $d>(n+1)\ma…

math.CV2024★ 1 cited

On the Gauss maps of complete minimal surfaces in $R^{n}$

Dinh Tuan Huynh

We prove that the Gauss map of a non-flat complete minimal surface immersed in $R^{n}$ can omit a generic hypersurface $D$ of degree at most $n^{n + 2} (n + 1)^{n + 2}$ .

math.CV2023

Entire holomorphic curves into $P^{n} (C)$ intersecting $n + 1$ general hypersurfaces

Zhangchi Chen, Dinh Tuan Huynh, Ruiran Sun +1

Let ${D_{i}}_{i = 1}^{n + 1}$ be $n + 1$ hypersurfaces in $P^{n} (C)$ with total degrees $\sum_{i = 1}^{n + 1} ° D_{i} ⩾ n + 2$ , in general position and satisfying a generic…

math.CV2023

Holomorphic mappings of maximal rank into projective spaces

Dinh Tuan Huynh

Let $1 \leq p \leq n$ be two positive integers. For a linearly nondegenerate holomorphic mapping $f : C^{p} \to P^{n} (C)$ of maximal rank intersecting…

math.CV2023★ 3 cited

Universal Entire Curves in Projective Spaces with Slow Growth

Zhangchi Chen, Dinh Tuan Huynh, Song-Yan Xie

We construct explicit universal entire curves in projective spaces whose Nevanlinna characteristic functions grow slower than any preassigned transcendental growth rate. Moreover,…

math.CV2021

On Ahlfors currents

Dinh Tuan Huynh, Song-Yan Xie

We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve $f: \m…

math.AG2020

Big Picard Theorem for jet differentials and Non-archimedean Ax-Lindemann Theorem

Dinh Tuan Huynh, Ruiran Sun, Song-Yan Xie

By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As app…

math.CV2020

On the Weyl-Ahlfors theory of derived curves

Dinh Tuan Huynh, Song-Yan Xie

For derived curves intersecting a family of decomposable hyperplanes in subgeneral position, we obtain an analog of Cartan-Nochka Second Main Theorem, generalizing a classical resu…

math.CV2020

Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator

Dinh Tuan Huynh, Lucas Kaufmann, Duc-Viet Vu

We study the Monge-Amp\` ere operator within the framework of Dinh-Sibony's intersection theory defined via density currents. We show that if $u$ is a plurisubharmonic function bel…

math.CV2019

On the set of divisors with zero geometric defect

Dinh Tuan Huynh, Duc-Viet Vu

Let $f : C \to X$ be a transcendental holomorphic curve into a complex projective manifold $X$ . Let $L$ be a very ample line bundle on $X$ . Let $s$ be a very generic holomo…

math.AG2017

Entire holomorphic curves into projective plane intersecting few generic algebraic curves

Dinh Tuan Huynh, Duc-Viet Vu, Song-Yan Xie

For $q \leq 3$ smooth plane algebraic curves $C_{i}$ having simple normal crossings, if the invariant logarithmic $2$ -jet differential bundle associated to $(\mathbb{P}^2(\m…

math.AG2017★ 5 cited

Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree

Dinh Tuan Huynh, Duc-Viet Vu, Song-Yan Xie

In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n…

math.CV2016

A geometric second main theorem

Julien Duval, Dinh Tuan Huynh

We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.

math.AG2016★ 6 cited

Construction of hyperbolic hypersurfaces of low degree in $p^{n} (c)$

Dinh Tuan Huynh

We construct families of hyperbolic hypersurfaces $X_{d} \subset P^{n + 1} (C)$ of degree $d \geq (\frac{n + 3}{2})^{2}$ .

math.CV2015

Examples of hyperbolic hypersurfaces of low degree in projective spaces

Dinh Tuan Huynh

We construct families of hyperbolic hypersurfaces of degree $2 n$ in the projective space $P^{n} (C)$ for $3 \leq n \leq 6$ .

A curvature estimate for holomophic maps on open Riemann surfaces

Vanishing of Invariant 2-Jet Differentials and Improved Hyperbolicity Degree Bounds in Dimension Two

A Second Main Theorem for Entire Curves Intersecting Three Conics

Some line and conic arrangements and their Waldschmidt constants

Some variants of the generalized Borel Theorem and applications

A p-adic Second Main Theorem

Degeneracy of holomorphic mappings into or avoiding Fermat type hypersurfaces

On the Gauss maps of complete minimal surfaces in Rn

Entire holomorphic curves into Pn(C) intersecting n+1 general hypersurfaces

Holomorphic mappings of maximal rank into projective spaces

Universal Entire Curves in Projective Spaces with Slow Growth

On Ahlfors currents

Big Picard Theorem for jet differentials and Non-archimedean Ax-Lindemann Theorem

On the Weyl-Ahlfors theory of derived curves

Intersection of (1,1)-currents and the domain of definition of the Monge-Ampere operator

On the set of divisors with zero geometric defect

Entire holomorphic curves into projective plane intersecting few generic algebraic curves

Entire holomorphic curves into projective spaces intersecting a generic hypersurface of high degree

A geometric second main theorem

Construction of hyperbolic hypersurfaces of low degree in pn(c)

Examples of hyperbolic hypersurfaces of low degree in projective spaces

A $p$ -adic Second Main Theorem

On the Gauss maps of complete minimal surfaces in $R^{n}$

Entire holomorphic curves into $P^{n} (C)$ intersecting $n + 1$ general hypersurfaces

Construction of hyperbolic hypersurfaces of low degree in $p^{n} (c)$