Sahil Gehlawat

activity

20202026

most citedTransformation formula for the Reduced Bergman kernel and its Application

4 citations · 5 across the 12 of their papers we have counts for

collaborators

13 papers

math.CV2026

Structural stability of the Jouanolou foliations in every degree

Sahil Gehlawat

We show that the degree $d$ Jouanolou foliation $J_{d}$ on $P^{2}$ is structurally stable for every $d \geq 2$ . We prove the existence of a neighbourhood $\mathcal U_d…

math.CV2026

A Canonical Positive Definite Kernel Associated with the $ξ$ -Bergman Kernel

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

Let $Ω \subset C^{n}$ and $ξ \in ℓ^{1}$ . The $ξ$ -Bergman kernel $K_{ξ, Ω}$ , introduced by Bao and Guan, generalizes the classical Bergman kernel by replacing the point ev…

math.CV2026

Stability of the Monomial Basis Kernel of Reinhardt domains

Shreedhar Bhat, Sahil Gehlawat

On a pseudoconvex Reinhardt domain $Ω \subset C^{n}$ the $p$ -Bergman space $A^{p} (Ω)$ admits a canonical basis of monomials indexed by a subset $S_{p} (Ω) \subset Z^{n}$ . The…

math.CV2025

Riemann surface foliations with non-discrete singular set

Sahil Gehlawat

Let $F$ be a singular Riemann surface foliation on a complex manifold $M$ , such that the singular set $E \subset M$ is non-discrete. We study the behavior of the foliatio…

math.CV2024

Generic singularities of holomorphic foliations by curves on $P^{n}$

Sahil Gehlawat, Viêt-Anh Nguyên

Let $F_{d} (P^{n})$ be the space of all singular holomorphic foliations by curves on $P^{n}$ ( $n \geq 2$ ) with degree $d \geq 1.$ We show that there is subset…

math.CV2024

A Note on Kernel Functions of Dirichlet Spaces

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

For a planar domain $Ω$ , we consider the Dirichlet spaces with respect to a base point $ζ \in Ω$ and the corresponding kernel functions. It is not known how these kernel functions be…

math.CV2023

Few remarks on the Poincaré metric on a singular holomorphic foliation

Sahil Gehlawat

Let $F$ be a Riemann surface foliation on $M ∖ E$ , where $M$ is a complex manifold and $E \subset M$ is a closed set. Assume that $F$ is hyperbolic, i.e…

math.CV2023

Regularity of the leafwise Poincare metric on singular holomorphic foliations

Sahil Gehlawat, Kaushal Verma

Let $F$ be a smooth Riemann surface foliation on $M ∖ E$ , where $M$ is a complex manifold and the singular set $E \subset M$ is an analytic set of codimension at l…

math.CV2022★ 1 cited

The Reduced Bergman Kernel and its Properties

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

In this article, we study some properties of the $n$ -th order weighted reduced Bergman kernels for planar domains, $n \geq 1$ . Specifically, we look at Ramadanov type theorems, loca…

math.CV2021★ 4 cited

Transformation formula for the Reduced Bergman kernel and its Application

Sahil Gehlawat, Aakanksha Jain, Amar Deep Sarkar

In this article, we prove the transformation formula for the reduced Bergman kernels under proper holomorphic correspondences between bounded domains in the complex plane. As a cor…

math.CV2021

Non-negative divisors and the Grauert metric

Sahil Gehlawat, Kaushal Verma

Grauert showed that it is possible to construct complete Kähler metrics on the complement of complex analytic sets in a domain of holomorphy. In this note, we study the holomorphic…

math.CV2020

Two remarks on the Poincaré metric on a singular Riemann surface foliation

Sahil Gehlawat, Kaushal Verma

Let $F$ be a smooth Riemann surface foliation on $M ∖ E$ , where $M$ is a complex manifold and $E \subset M$ is a closed set. Fix a hermitian metric $g$ on $M \set…

math.CV2020

On Grauert's examples of complete Kähler metrics

Sahil Gehlawat, Kaushal Verma

Grauert showed that the existence of a complete Kähler metric does not characterize domains of holomorphy by constructing such metrics on the complements of complex analytic sets i…

Structural stability of the Jouanolou foliations in every degree

A Canonical Positive Definite Kernel Associated with the ξ-Bergman Kernel

Stability of the Monomial Basis Kernel of Reinhardt domains

Riemann surface foliations with non-discrete singular set

Generic singularities of holomorphic foliations by curves on Pn

A Note on Kernel Functions of Dirichlet Spaces

Few remarks on the Poincaré metric on a singular holomorphic foliation

Regularity of the leafwise Poincare metric on singular holomorphic foliations

The Reduced Bergman Kernel and its Properties

Transformation formula for the Reduced Bergman kernel and its Application

Non-negative divisors and the Grauert metric

Two remarks on the Poincaré metric on a singular Riemann surface foliation

On Grauert's examples of complete Kähler metrics

A Canonical Positive Definite Kernel Associated with the $ξ$ -Bergman Kernel

Generic singularities of holomorphic foliations by curves on $P^{n}$