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Ozcan Yazici

Publications and source records attributed to Ozcan Yazici.

8 recordsLinked to original sources
arXiv2026

$α$-Hölder Integrability Exponent

For a plurisubharmonic function $φ$ on $Ω\subset \mathbb C^n$ we defined $α$-Hölder integrability exponent $c_α(φ)$ and obtained a lower bound in terms of Lelong number $ν(φ)$ and intersection numbers $e_j(φ)$. This lower bound improves the earlier result of Kaufmann \cite{Kf} on the integrability of plurisubharmonic functions with respect to Monge-Ampére measure with $α$-Hölder continuous potentials. We also give a sharp lower bound for $α$-Hölder integrability exponent of certain type of plurisubharmonic functions.

math.CV↗
arXiv2023

Upper level sets of Lelong numbers on Hirzebruch surfaces

Let $\mathbb F_a$ denote the Hirzebruch surfaces and $\mathcal{T}_{α,α^{\prime}}(\mathbb{F}_{a})$ denotes the set of positive, closed $(1,1)$-currents on $\mathbb{F}_{a}$ whose cohomology class is $αF+α^{\prime} H$ where $F$ and $H$ generates the Picard group of $\mathbb F_a$. $E^+_β(T)$ denotes the upper level sets of Lelong numbers $ν(T,x)$ of $T\in \mathcal{T}_{α,α^{\prime}}(\mathbb{F}_{a})$. When $a=0$, ($\mathbb F_a=\mathbb P^1\times \mathbb P^1$), for any current $T\in \mathcal T_{α,α'}(\mathbb P^1\times \mathbb P^1)$, we show that $E^{+}_{(α+α')/3}(T)$ is contained in a curve of total degree $2$, possibly except $1$ point. For any current $T\in \mathcal T_{α,α'}(\mathbb F_a)$, we show that $ E^{+}_β(T)$ is contained in either in a curve of bidegree $(0,1)$ or in $a+1$ curves of bidegree $(1,0)$ where $β\geq (α+ (a+1)α^{\prime})/(a+2)$.

math.CV↗
arXiv2023

Local boundedness of Catlin q-type

In [6], D'Angelo introduced the notion of finite type for points $p$ of a real hypersurface $M$ of $\mathbb C^n$ by defining the order of contact $Δ_q(M,p)$ of complex analytic $q$-dimensional varieties with $M$ at $p$. Later, Catlin [4] defined $q$-type, $D_q(M,p)$ for points of hypersurfaces by considering generic $(n-q+1)$-dimensional complex affine subspaces of $\mathbb C^n$. We define a generalization of the Catlin's $q$-type for an arbitrary subset $M$ of $\mathbb C^n$ in a similar way that D'Angelo's 1-type, $Δ_1(M,p)$, is generalized in [13]. Using recent results connecting the D'Angelo and Catlin $q$-types in [1] and building on D'Angelo's work on the openness of the set of points of finite $Δ_q$-type, we prove the openness of the set of points of finite Catlin $q$-type for an arbitrary subset $M\subset \mathbb C^n$.

math.CV↗
arXiv2020

Finite Type Points On Subsets Of $\mathbb C^n$

In [4], D'Angelo introduced the notion of points of finite type for a real hypersurface $M$ in $\mathbb C^n$ and showed that the set of points of finite type in $M$ is open. Later, Lamel-Mir [8] considered a natural extension of D'Angelo's definition for an arbitrary set $M$ in $\mathbb C^n$. Building on D'Angelo's work, we prove the openness of the set of points of finite type for any subset $M$ in $ \mathbb C^n.$

math.CV↗
arXiv2019

Holomorphic extension of meromorphic mappings along real analytic hypersurfaces

Let $M\subset \mathbb C^n$ be a real analytic hypersurface, $M'\subset \mathbb C^N$ $(N\geq n)$ be a strongly pseudoconvex real algebraic hypersurface of the special form and $F$ be a meromorphic mapping in a neighborhood of a point $p\in M$ which is holomorphic in one side of $M$. Assuming some additional conditions for the mapping $F$ on the hypersurface $M$, we proved that $F$ has a holomorphic extension to $p$. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensions.

math.CV↗
arXiv2015

Extension of Plurisubharmonic Functions in the Lelong Class

Let $X$ be an algebraic subvariety of $\mathbb C^n$ and $\bar X$ be its closure in $\mathbb P^n.$ In their paper \cite{CGZ} Coman-Guedj-Zeriahi proved that any plurisubharmonic function with logarithmic growth on $X$ extends to a plurisubharmonic function with logarithmic growth on $\mathbb C^n$ when the germs $(\bar X,a)$ in $\mathbb P^n$ are irreducible for all $a\in \bar X\setminus X.$ In this paper we consider $X$ for which the germ $(\bar X,a)$ is reducible for some $a\in \bar X\setminus X$ and we give a necessary and sufficient condition for $X$ so that any plurisubharmonic function with logarithmic growth on $X$ extends to a plurisubharmonic function with logarithmic growth on $\mathbb C^n.$

math.CV↗