KAUSHAL VERMA
Articles written in Proceedings – Mathematical Sciences
Volume 116 Issue 1 February 2006 pp 59-70
Boundary regularity of correspondences in ℂ^{n}
Let
Volume 128 Issue 1 February 2018 Article ID 0010 Research Article
Some aspects of shift-like automorphisms of $\mathbb{C}^{k}$
The goal of this article is two fold. First, using transcendental shift-like automorphisms of $\mathbb{C}^{k} , k \geq 3$ we construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of $\mathbb{C}^{k} , k \geq 3$ whose range avoids a given polydisc but contains the complement of a slightly larger concentric polydisc. This generalizes a result of Dixon–Esterle in $\mathbb{C}^{2}$. The second example shows the existence of a Fatou–Bieberbach domain in $\mathbb{C}^{k} , k \geq 3$ that is constrained to lie in a prescribed region. This is motivated by similar results of Buzzard and Rosay–Rudin. In the second part we compute the order and type of entire mappings that parametrize one dimensional unstable manifolds for shift-like polynomial automorphisms and show how they can be used to prove a Yoccoz type inequality for this class of automorphisms.
Volume 130 All articles Published: 15 June 2020 Article ID 0035 Research Article
A submultiplicative property of the Carathéodory metric on planar domains
AMAR DEEP SARKAR KAUSHAL VERMA
Given a pair of smoothly bounded domains $D_{1}$, $D_{2} \subset \mathbb{C}$, the purpose of this paper is to obtain an inequality that relates the Carathéodory metrics on $D_{1}$, $D_{2}$, $D_{1}\cap D_{2}$ and $D_{1} \cup D_{2}$.
Volume 130, 2020
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