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  • Examples of non-autonomous basins of attraction 
    Bera, Sayani; PAL, RATNA; Verma, Kaushal (Project Euclid, 2017)
    The purpose of this paper is to present several examples of non-autonomous basins of attraction that arise from sequences of automorphisms of Ck. In the first part, we prove that the non-autonomous basin of attraction ...
  • Ergodic properties of families of H-non maps 
    PAL, RATNA; Verma, Kaushal (Polskiej Akademii Nauk, Instytut Matematyczny, 2018-06)
    Let {Hλ} be a continuous family of Hénon maps parametrized by λ∈M, where M⊂Ck is compact. The purpose of this paper is to understand some aspects of the random dynamical system obtained by iterating maps from this family. ...
  • Comments on the Green’s function of a planar domain 
    BORAH, DIGANTA; Haridas, Pranav; Verma, Kaushal (Springer Nature, 2018-09)
    We study several quantities associated to the Green’s function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and 𝐿2-cohomology of the capacity ...
  • A rigidity theorem for Hénon maps 
    Bera, Sayani; PAL, RATNA; Verma, Kaushal (Springer Nature, 2019-03)
    The purpose of this note is twofold. First, we study the relation between a pair of Hénon maps that share the same forward and backward non-escaping sets. Second, it is shown that there exists a continuum of ShortC2’s that ...
  • Remarks on the Higher Dimensional Suita Conjecture 
    Balakumar, G. P.; BORAH, DIGANTA; Mahajan, Prachi; Verma, Kaushal (American Mathematical Society, 2019-08)
    To study the analog of Suita's conjecture for domains D subset of C-n, n >= 2, Blocki introduced the invariant F-D(k) (z) = K-D(z)lambda(I-D(k) (z)), where K-D(z) is the Bergman kernel of D along the diagonal and lambda(I-D(k) ...
  • Further remarks on the higher dimensional Suita conjecture 
    Balakumar, G. P.; BORAH, DIGANTA; Mahajan, Prachi; Verma, Kaushal (The Institute of Mathematics of the Polish Academy of Sciences, 2020-07)
    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 ...
  • Narasimhan–Simha-type metrics on strongly pseudoconvex domains in 
    BORAH, DIGANTA; Verma, Kaushal (Talor & Francis, 2022-05)
    For a bounded domain D⊂Cn, let KD=KD(z)>0 denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on D that are square integrable with respect to the weight K−dD, ...
  • Limits of an increasing sequence of complex manifolds 
    Balakumar, G. P.; BORAH, DIGANTA; Mahajan, Prachi; Verma, Kaushal (Springer Nature, 2023-06)
    Let M be a complex manifold which admits an exhaustion by open subsets Mj each of which is biholomorphic to a fixed domain Ω⊂Cn. The main question addressed here is to describe M in terms of Ω. Building on work of ...

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