Kaushal Verma - Academia.edu (original) (raw)

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Papers by Kaushal Verma

The Michigan Mathematical Journal, 2001

$Research paper thumbnail of Boundary regularity of correspondences in <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="bold">C</mi><mn mathvariant="bold">2</mn></msup></mrow><annotation encoding="application/x-tex">{\bf C^2}</annotation></semantics></math>C2$

Mathematische Zeitschrift, 1999

In this section D and D will denote arbitrary bounded domains in C n unless stated otherwise. Wri... more In this section D and D will denote arbitrary bounded domains in C n unless stated otherwise. Write z ∈ C n as z = ( z, z n ) where z denotes the first n − 1 coordinates of z; and a neighbourhood U z of z as U z = U z × U z,n ⊂ C n−1 z × C 1 zn . For p ∈ C n , B(p, r) will denote the euclidean ball of radius r with centre at p and for η ∈ (0, 1), ηB(p, r) is a ball with radius ηr

Journal of Geometric Analysis, 2003

Let f : D → D ′ be a proper holomorphic mapping between bounded domains D, D ′ in C 2 . Let M, M ... more Let f : D → D ′ be a proper holomorphic mapping between bounded domains D, D ′ in C 2 . Let M, M ′ be open pieces on ∂D, ∂D ′ respectively that are smooth, real analytic and of finite type. Suppose that the cluster set of M under f is contained in M ′ . It is shown that f extends holomorphically across M . This can be viewed as a local version of the Diederich-Pinchuk extension result for proper mappings in C 2 .

$Research paper thumbnail of Holomorphic Mappings between Domains in <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">C</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathbb C^2</annotation></semantics></math>C2$

Canadian Journal of Mathematics, 2012

Complex Variables, 2004

Let be a smoothly bounded real analytic domain in and a compact subgroup of , its holomorphic aut... more Let be a smoothly bounded real analytic domain in and a compact subgroup of , its holomorphic automorphism group. It is shown that each element g of extends to a neighborhood of that is independent of g.

Advances in Mathematics, 2013

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclid... more We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded domains. It is shown that such mappings extend smoothly up to the closures of the domains, provided each factor of the source satisfies Condition R. It also shown that the number of smoothly bounded factors in the source and target must be the same, and the proper holomorphic map splits as product of proper mappings between the factor domains.