Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

Department of Mathematics

arXiv preprint arXiv:2103.

Structure theorems for Power Series in Several Complex Variables

World University root node

arXiv preprint arXiv:2108.

Limits of an increasing sequence of complex manifolds

For a domain D ⊂ Cn, n ≥ 2, let FkD(z) = KD(z)λ(IkD(z)), where KD(z) is the Bergman kernel of D along the diagonal and λ(IkD(z)) is the Lebesgue measure of the Kobayashi indicatrix at the point z. This biholomorphic invariant was introduced by Błocki. We study its limiting boundary behaviour on two classes of domains: h-extendible and strongly pseudoconvex polyhedral domains. © Instytut Matematyczny PAN, 2020.

Annales Polonici Mathematici

Further remarks on the higher dimensional suita conjecture

To study the analog of Suita'fs conjecture for domains ⊂Cn, n ≥ 2, Blocki introduced the invariant Fκ D (z) = KD(z)λIκ D(z), where KD (z) is the Bergman kernel of D along the diagonal and λIκ D(z) is the Lebesgue measure of the Kobayashi indicatrix at the point z. In this note, we study the behaviour of Fκ D (z) (and other similar invariants using different metrics) on strongly pseudconvex domains and also compute its limiting behaviour explicitly at certain points of decoupled egg domains in C2. © 2019 American Mathematical Society.

Proceedings of the American Mathematical Society

Remarks on the higher dimensional suita conjecture

We study the Wu metric on convex egg domains of the form where m &gt; 1/2, m ≠ 1. The Wu metric is shown to be real analytic everywhere except on a lower dimensional subvariety where it fails to be C2-smooth. Overall however, the Wu metric is shown to be continuous when m = 1/2 and even c1-smooth for each m &gt; 1/2, and in all cases, a non-Kähler Hermitian metric with its holomorphic curvature strongly negative in the sense of currents. This gives a natural answer to a conjecture of S. Kobayashi and H. Wu for such E2m.

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Analysing the Wu metric on a class of eggs in Cn -1

We study the Wu metric for the non-convex domains of the form E2m = (z ∈ ℂn: |z1|2m + |z2|2 + · · · + |zn-1|2 + |zn|2 &lt; 1), where 0 &lt; m &lt; 1/2. We give explicit expressions for the Kobayashi metric and the Wu metric on such pseudoeggs E2m. We verify that the Wu metric is a continuous Hermitian metric on E2m, real analytic everywhere except along the complex hypersurface Z = ((0, z2, . . . , zn) ∈ E2m). We also show that the holomorphic curvature of the Wu metric for this noncompact family of pseudoconvex domains is bounded above in the sense of currents by a negative constant independent of m. This verifies a conjecture of S. Kobayashi and H. Wu for such E2m. © Indian Academy of Sciences.

Analysing the Wu metric on a class of eggs in ℂn - II

The purpose of this article is to provide an exposition of domains of convergence of power series of several complex variables without recourse to relatively advanced notions of convexity.

arXiv preprint arXiv:1601.

Power Series in Several Complex Variables

Annales de la Facult{\'{e}} des sciences de Toulouse : Math{\'{e}}matiques

Bounds for invariant distances on pseudoconvex Levi corank one domains and applications

Rigidity And Regularity Of Holomorphic Mappings

It is shown that every hyperbolic rigid polynomial domain in ℂ3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight. © 2014 Copyright Taylor &amp; Francis Group, LLC.

Complex Variables and Elliptic Equations

Model domains in ℂ3 with abelian automorphism group

The purpose of this article is to study Lipschitz CR mappings from an h-extendible (or semi-regular) hypersurface in ℂn. Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudoconvex domains is also proved. © 2012 Springer-Verlag.