Pradip Kumar

activity

20232026

collaborators

12 papers

math.DG2026

On the complete maximal maps and their singularities

Rivu Bardhan, Indranil Biswas, Pradip Kumar +1

This article investigates the global structure of maximal surfaces (space-like immersions with zero mean curvature) in Lorentz-Minkowski $3$ -space $E_{1}^{3}$ , especially focu…

math.QA2026

Holomorphic Jet Modules and Holomorphic Connections for Noncommutative Complex Curves

Indranil Biswas, Satyajit Guin, Pradip Kumar

We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $…

math.AG2026

Logarithmic spectral correspondence for $V$ --twisted Higgs bundles on punctured curves

Pradip Kumar

Let $X$ be a smooth projective complex curve, $P \subset X$ a reduced effective divisor, and $X^{0} = X ∖ P$ . We study logarithmic $V$ -twisted Higgs bundles arising from a loga…

math.DG2026

Finite-energy equivariant minimal immersions in $CH^{2}$ with fixed-lift proper cusp ends

Indranil Biswas, Pradip Kumar, John Loftin

Let $Σ_{0} = Σ ∖ {z_{1}, \dots, z_{n}}$ be a finite-type hyperbolic Riemann surface, with its universal cover being identified with $H$ . We prove that a finite-ener…

math.AG2026

Lie algebroid connection and Harder-Narasimhan reduction

Ashima Bansal, Indranil Biswas, Pradip Kumar

Take a holomorphic Lie algebroid $(V, ϕ)$ on a compact connected Riemann surface $X$ such that the anchor map $ϕ$ is not surjective. Let $P$ be a parabolic subgroup of a complex…

math.QA2026

Fixed points and Holomorphic Structures on Line Bundles over the Quantum Projective Line

Indranil Biswas, Satyajit Guin, Pradip Kumar

It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree…

math.DG2025

Higher genus Angel surfaces

Rivu Bardhan, Indranil Biswas, Shoichi Fujimori +1

We prove the existence of complete minimal surfaces in $R^{3}$ of arbitrary genus $p \geq 1$ and least total absolute curvature with precisely two ends -- one catenoidal…

math.AG2025

A criterion for holomorphic Lie algebroid connections

David Alfaya, Indranil Biswas, Pradip Kumar +1

Given a holomorphic Lie algebroid $(V, ϕ)$ on a compact connected Riemann surface $X$ , we give a necessary and sufficient condition for a holomorphic vector bundle $E$ on $X$ to ad…

math.AG2025

Remarks on Higgs bundles twisted by a vector bundle

David Alfaya, Indranil Biswas, Pradip Kumar

For any V-twisted Higgs bundle on a compact Riemann surface X, where V is a holomorphic vector bundle of rank two on X, there are two associated Higgs bundles on X, twisted by line…

math.AG2024

A criterion for Lie algebroid connections on a compact Riemann surface

Indranil Biswas, Pradip Kumar, Anoop Singh

Let $X$ be a compact connected Riemann surface and $(V, ϕ)$ a holomorphic Lie algebroid on $X$ such that the holomorphic vector bundle $V$ is stable. We give a necessary and suffic…

math.AG2024

Parabolic vector bundles and Lie algebroid connections

David Alfaya, Indranil Biswas, Pradip Kumar +1

Given a holomorphic Lie algebroid on an m-pointed Riemann surface, we define parabolic Lie algebroid connections on any parabolic vector bundle equipped with parabolic structure ov…

math.DG2023

Higher genus maxfaces with Enneper end

Rivu Bardhan, Indranil Biswas, Pradip Kumar

We have proven the existence of new higher-genus maxfaces with Enneper end. These maxfaces are not the companions of any existing minimal surfaces, and furthermore, the singularity…