Saikat Mazumdar

activity

20152026

most citedGJMS-type Operators on a compact Riemannian manifold: Best constants and Coron-type solutions

21 citations · 34 across the 14 of their papers we have counts for

collaborators

15 papers

math.DG2026

Barycenter technique for the higher order $Q$ -curvature equation

Saikat Mazumdar, Cheikh Birahim Ndiaye

Let $k \geq 1$ be an integer, and $(M, g)$ be a smooth, closed Riemannian manifold of dimension $2 k + 1 \leq n \leq 2 k + 3$ , or $(M, g)$ be locally conformally flat of dimension $n \geq 2 k + 1$ . Ap…

math.AP2025

Compactness of conformal metrics with constant $Q$ -curvature of higher order

Saikat Mazumdar, Bruno Premoselli

Let $k \geq 1$ be a positive integer and let $P_{g}$ be the GJMS operator $P_{g}$ of order $2 k$ on a closed Riemannian manifold $(M, g)$ of dimension $n > 2 k$ . We investigate the compactne…

math.AP2025

Compactness for the Hardy-Sobolev equation on manifolds

Hussein Cheikh Ali, Saikat Mazumdar

Let $(M, g)$ be a closed Riemannian manifold of dimension $n \geq 3$ , and let $h \in C^{1} (M)$ be such that the operator $Δ_{g} + h$ is coercive. Fix $x_{0} \in M$ and $s \in (0, 2)$ . We…

math.AP2022

Sharp quantitative stability of Struwe's decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space: Part I

Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar +1

A classical result owing to Mancini and Sandeep [Ann. Sc. Norm. Super. Pisa Cl. Sci. 7 (2008)] asserts that all positive solutions of the Poincaré-Sobolev equation on the hyperboli…

math.AP2022

Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows

Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar +1

Consider the Poincaré-Sobolev inequality on the hyperbolic space: for every $n \geq 3$ and $1 < p \leq \frac{n + 2}{n - 2},$ there exists a best constant $S_{n, p, λ} (B^{n}) > 0$ …

math.AP2022

Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up

Debdip Ganguly, Debabrata Karmakar, Saikat Mazumdar

We consider the following Cauchy problem for the semi linear heat equation on the hyperbolic space: \begin{align}\label{abs:eqn} \left\{\begin{array}{ll} \partial_{t}u=Δ_{\mathbb{H…

math.AP2021

Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold

Saikat Mazumdar, Jérôme Vétois

On a smooth, closed Riemannian manifold, we study the question of proportionality of components, also called synchronization, of vector-valued solutions to nonlinear elliptic Schrö…

math.AP2021★ 6 cited

Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds

J. Flynn, N. Lam, G. Lu +1

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the ex…

math.AP2020

Existence results for the higher-order $Q$ -curvature equation

Saikat Mazumdar, Jérôme Vétois

We obtain existence results for the $Q$ -curvature equation of order $2 k$ on a closed Riemannian manifold of dimension $n \geq 2 k + 1$ , where $k \geq 1$ is an integer. We obtain these resu…

math.AP2019★ 4 cited

Multiplicity and stability of the Pohozaev obstruction for Hardy-Schrödinger equations with boundary singularity

Nassif Ghoussoub, Saikat Mazumdar, Frédéric Robert

Let $Ω$ be a smooth bounded domain in $R^{n}$ ( $n \geq 3$ ) such that $0 \in \partial Ω$ . In this memoir, we consider issues of non-existence, existence, and multiplicity of var…

math.AP2018

The Hardy--Schrödinger Operator on the Poincaré Ball: Compactness and Multiplicity

Nassif Ghoussoub, Saikat Mazumdar, Frédéric Robert

Let $Ω$ be a compact smooth domain containing zero in the Poincaré ball model of the Hyperbolic space $B^{n}$ ( $n \geq 3$ ) and let $- Δ_{B^{n}}$ be the Laplace-Bel…

math.AP2017★ 3 cited

Mass and Extremals Associated with the Hardy-Schrödinger Operator on Hyperbolic Space

Hardy Chan, Nassif Ghoussoub, Saikat Mazumdar +2

We consider the Hardy-Schrödinger operator $- Δ_{B^{n}} - γ V_{2}$ on the Poincaré ball model of the Hyperbolic space $B^{n}$ ( $n \geq 3$ ). Here $V_{2}$ is a well chosen…

math.AP2017

Hardy-Sobolev equations with asymptotically vanishing singularity: Blow-up analysis for the minimal energy

Saikat Mazumdar

We study the asymptotic behavior of a sequence of positive solutions $(u_{ε})_{ε > 0}$ as $ε \to 0$ to the family of equations \begin{equation*} \left\{\begin{array}{ll} Δu_ε+a(x)u_ε= \…

math.AP2016

Struwe's Decomposition for a Polyharmonic Operator on a compact Riemannian Manifold with or without Boundary

Saikat Mazumdar

Given a high-order elliptic operator on a compact manifold with or without boundary, we perform the decomposition of Palais-Smale sequences for a nonlinear problem as a sum of bubb…

math.AP2015★ 21 cited

GJMS-type Operators on a compact Riemannian manifold: Best constants and Coron-type solutions

Saikat Mazumdar

In this paper we investigate the existence of solutions to a nonlinear elliptic problem involving critical Sobolev exponent for a polyharmonic operator on a Riemannian manifold $M$ …

Barycenter technique for the higher order Q-curvature equation

Compactness of conformal metrics with constant Q-curvature of higher order

Compactness for the Hardy-Sobolev equation on manifolds

Sharp quantitative stability of Struwe's decomposition of the Poincaré-Sobolev inequalities on the hyperbolic space: Part I

Sharp quantitative stability of Poincare-Sobolev inequality in the hyperbolic space and applications to fast diffusion flows

Non-linear heat equation on the Hyperbolic space: Global existence and finite-time Blow-up

Non-synchronized solutions to nonlinear elliptic Schrödinger systems on a closed Riemannian manifold

Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds

Existence results for the higher-order Q-curvature equation

Multiplicity and stability of the Pohozaev obstruction for Hardy-Schrödinger equations with boundary singularity

The Hardy--Schrödinger Operator on the Poincaré Ball: Compactness and Multiplicity

Mass and Extremals Associated with the Hardy-Schrödinger Operator on Hyperbolic Space

Hardy-Sobolev equations with asymptotically vanishing singularity: Blow-up analysis for the minimal energy

Struwe's Decomposition for a Polyharmonic Operator on a compact Riemannian Manifold with or without Boundary

GJMS-type Operators on a compact Riemannian manifold: Best constants and Coron-type solutions

Barycenter technique for the higher order $Q$ -curvature equation

Compactness of conformal metrics with constant $Q$ -curvature of higher order

Existence results for the higher-order $Q$ -curvature equation