Diganta Borah

activity

20102026

most citedSome remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains

5 citations · 16 across the 13 of their papers we have counts for

collaborators

14 papers

math.CV2026

A quasiconformal variant of the union problem

Diganta Borah, Prachi Mahajan, Kaushal Verma

The Union Problem, which has its genesis in the classical Levi problem, asks for a classification of complex manifolds $M$ that can be exhausted by an increasing union of submanifo…

math.CV2024

Some remarks on the Carathéodory and Szegö metrics on planar domains

Anjali Bhatnagar, Diganta Borah

We study several intrinsic properties of the Carathéodory and Szegö metrics on finitely connected planar domains. Among them are the existence of closed geodesics and geodesic spir…

math.CV2024

Limits of an increasing sequence of Riemann surfaces

Diganta Borah, Prachi Mahajan, Jiju Mammen

Let $M$ be a Riemann surface which admits an exhaustion by open subsets $M_{j}$ each of which is biholomorphic to a fixed domain $Ω \subset C$ . We describe $M$ in terms of $Ω…

math.CV2023★ 2 cited

The squeezing function: exact computations, optimal estimates, and a new application

Gautam Bharali, Diganta Borah, Sushil Gorai

We present a new application of the squeezing function $s_{D}$ , using which one may detect when a given bounded pseudoconvex domain $D  C^{n}$ , $n \geq 2$ , is not b…

math.CV2021★ 5 cited

Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains

Diganta Borah, Debaprasanna Kar

The Ricci curvature of the Bergman metric on a bounded domain $D \subset C^{n}$ is strictly bounded above by $n + 1$ and consequently $lo g (K_{D}^{n + 1} g_{B, D})$ , where $K_{D}$ is…

math.CV2021★ 2 cited

Limits of an increasing sequence of complex manifolds

G. P. Balakumar, Diganta Borah, Prachi Mahajan +1

Let $M$ be a complex manifold which admits an exhaustion by open subsets $M_{j}$ each of which is biholomorphic to a fixed domain $Ω \subset C^{n}$ . The main question addressed…

math.CV2021★ 2 cited

Narasimhan--Simha type metrics on strongly pseudoconvex domains in $C^{n}$

Diganta Borah, Kaushal Verma

For a bounded domain $D \subset C^{n}$ , let $K_{D} = K_{D} (z) > 0$ denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic fun…

math.CV2018★ 1 cited

Further remarks on the higher dimensional Suita conjecture

G. P. Balakumar, Diganta Borah, Prachi Mahajan +1

For a domain $D \subset C^{n}$ , $n \geq 2$ , let $F_{D}^{k} (z) = K_{D} (z) λ (I_{D}^{k} (z))$ , where $K_{D} (z)$ is the Bergman kernel of $D$ along the diagonal and $λ (I_{D}^{k} (z))$ …

math.CV2018

Remarks on the higher dimensional Suita conjecture

G. P. Balakumar, Diganta Borah, Prachi Mahajan +1

To study the analog of Suita's conjecture for domains $D \subset C^{n}$ , $n \geq 2$ , Błocki introduced the invariant $F_{D}^{k} (z) = K_{D} (z) λ (I_{D}^{k} (z))$ , where $K_{D} (z)$ is t…

math.NT2017★ 4 cited

Arakelov Self-intersection numbers of minimal regular models of modular curves $X_{0} (p^{2})$

Debargha Banerjee, Diganta Borah, Chitrabhanu Chaudhuri

We compute an asymptotic expression for the Arakelov self-intersection number of the relative dualizing sheaf of Edixhoven's minimal regular model for the modular curve $X_{0} (p^{2})$ …

math.CV2016

Comments on the Green's function of a planar domain

Diganta Borah, Pranav Haridas, Kaushal Verma

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, curv…

math.CV2014

Remarks on the metric induced by the Robin function III

Diganta Borah

Let $D$ be a smoothly bounded pseudoconvex domain in $C^{n}$ , $n > 1$ . Using the Robin function $Λ (p)$ that arises from the Green function $G (z, p)$ for $D$ with pole at $p \…

math.CV2012

Remarks on the metric induced by the Robin function II

Diganta Borah

Let $D$ be a smoothly bounded pseudoconvex domain in $C^{n}$ , $n > 1$ . Using the Robin function $\La(p)$ that arises from the Green function $G (z, p)$ for $D$ with pole at $p…

math.CV2010

Remarks on the metric induced by the Robin function

Diganta Borah, Kaushal Verma

Let $D$ be a smoothly bounded pseudoconvex domain in $C^{n}$ , $n > 1$ . Using $G (z, p)$ , the Green function for $D$ with pole at $p \in D$ associated with the standard sum-of-…

A quasiconformal variant of the union problem

Some remarks on the Carathéodory and Szegö metrics on planar domains

Limits of an increasing sequence of Riemann surfaces

The squeezing function: exact computations, optimal estimates, and a new application

Some remarks on the Kobayashi--Fuks metric on strongly pseudoconvex domains

Limits of an increasing sequence of complex manifolds

Narasimhan--Simha type metrics on strongly pseudoconvex domains in Cn

Further remarks on the higher dimensional Suita conjecture

Remarks on the higher dimensional Suita conjecture

Arakelov Self-intersection numbers of minimal regular models of modular curves X0​(p2)

Comments on the Green's function of a planar domain

Remarks on the metric induced by the Robin function III

Remarks on the metric induced by the Robin function II

Remarks on the metric induced by the Robin function

Narasimhan--Simha type metrics on strongly pseudoconvex domains in $C^{n}$

Arakelov Self-intersection numbers of minimal regular models of modular curves $X_{0} (p^{2})$