• KAUSHAL VERMA

Articles written in Proceedings – Mathematical Sciences

• Boundary regularity of correspondences in ℂn

LetM, M′ be smooth, real analytic hypersurfaces of finite type in ℂn and$$\hat f$$ a holomorphic correspondence (not necessarily proper) that is defined on one side ofM, extends continuously up toM and mapsM to M′. It is shown that$$\hat f$$ must extend acrossM as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich-Pinchuk extension result for CR maps.

• 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.

• A submultiplicative property of the Carathéodory metric on planar domains

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 $D_{1} \cup D_{2}$.

• Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
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• Editorial Note on Continuous Article Publication

Posted on July 25, 2019