Do you want to publish a course? Click here

On minimal Rolles domains for complex polynomials

126   0   0.0 ( 0 )
 Added by Michael Miller
 Publication date 2009
  fields
and research's language is English




Ask ChatGPT about the research

Define a subset of the complex plane to be a Rolles domain if it contains (at least) one critical point of every complex polynomial P such that P(-1)=P(1). Define a Rolles domain to be minimal if no proper subset is a Rolles domain. In this paper, we investigate minimal Rolles domains.



rate research

Read More

117 - Franc Forstneric 2021
In this paper we find big Euclidean domains in complex manifolds. We consider open neighbourhoods of sets of the form $Kcup M$ in a complex manifold $X$, where $K$ is a compact $mathscr O(U)$-convex set in an open Stein neighbourhood $U$ of $K$, $M$ is an embedded Stein submanifold of $X$, and $Kcap M$ is compact and $mathscr O(M)$-convex. We prove a Docquier-Grauert type theorem concerning biholomorphic equivalence of neighbourhoods of such sets, and we give sufficient conditions for the existence of Stein neighbourhoods of $Kcup M$, biholomorphic to domains in $mathbb C^n$ with $n=dim X$, such that $M$ is mapped onto a closed complex submanifold of $mathbb C^n$.
A complex manifold $X$ is emph{weakly complete} if it admits a continuous plurisubharmonic exhaustion function $phi$. The minimal kernels $Sigma_X^k, k in [0,infty]$ (the loci where are all $mathcal{C}^k$ plurisubharmonic exhaustion functions fail to be strictly plurisubharmonic),introduced by Slodkowski-Tomassini, and the Levi currents, introduced by Sibony, are both concepts aimed at measuring how far $X$ is from being Stein. We compare these notions, prove that all Levi currents are supported by all the $Sigma_X^k$s, and give sufficient conditions for points in $Sigma_X^k$ to be in the support of some Levi current. When $X$ is a surface and $phi$ can be chosen analytic, building on previous work by the second author, Slodkowski, and Tomassini,we prove the existence of a Levi current precisely supported on $Sigma_X^infty$, and give a classification of Levi currents on $X$. In particular,unless $X$ is a modification of a Stein space, every point in $X$ is in the support of some Levi current.
58 - Naveen Gupta 2018
This is an expository survey of the Jacobian problem for the class of Pluriharmonic functions.
143 - David E. Barrett 2011
We show that the efficiency of a natural pairing between certain projectively invariant Hardy spaces on dual strongly C-linearly convex real hypersurfaces in complex projective space is measured by the norm of the corresponding Leray transform.
114 - XiaoHuang Huang 2021
In this paper, we study the uniqueness of the differential polynomials of entire functions. We prove the following result: Let $f(z)$ be a nonconstant entire function on $mathbb{C}^{n}$ and $g(z)=b_{-1}+sum_{i=0}^{n}b_{i}D^{k_{i}}f(z)$, where $b_{-1}$ and $b_{i} (i=0ldots,n)$ are small meromorphic functions of $f$, $k_{i}geq0 (i=0ldots,n)$ are integers. Let $a_{1}(z) otequivinfty, a_{2}(z) otequivinfty$ be two distinct small meromorphic functions of $f(z)$. If $f(z)$ and $g(z)$ share $a_{1}(z)$ CM, and $a_{2}(z)$ IM. Then either $f(z)equiv g(z)$ or $a_{1}=2a_{1}=2$, $$f(z)equiv e^{2p}-2e^{p}+2,$$ and $$g(z)equiv e^{p},$$ where $p(z)$ is a non-constant entire function on $mathbb{C}^{n}$.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا