Publications 

Published / To Appear

• Hardy and Rellich identities and inequalities for Grushin operators via spherical vector fields, 

(K. Jotsaroop, P. Roychowdhury), 

To appear in  Ann. Sc. Norm. Super. Pisa Cl. Sci., (arXiv: 2404.05510). 

•  Poincaré-Sobolev equations with the critical exponent and potential in the hyperbolic space, 

 (with M. Bhakta, D. Gupta, A. Sahoo), 

  To appear in Proceedings of the Royal Society of Edinburgh: Section A, (2024, arXiv: 2410.03164).

•  Conformally invariant equations with negative critical exponents on the three dimensional hyperbolic space, 

  (with J. Li, G. Lu, J. Wang),  

   Calculus of Variations and Partial Differential Equations, 65 (2026), no. 9, Paper No. 248.

•  Sharp quantitative stability of Struwe’s decomposition of the Poincaré–Sobolev inequalities on the hyperbolic space
  (with M. Bhakta, D. Karmakar, S. Mazumdar)
  Advances in Mathematics 479 (2025), Paper No. 110447.

•  Fractional Schrödinger equations with mixed nonlinearities: asymptotic profiles, uniqueness and nondegeneracy of ground states
  (with M. Bhakta, P. Das)
  Journal of Geometric Analysis 35 (2025), no. 8, Paper No. 245.

•  Sharp quantitative stability of Poincaré–Sobolev inequality in the hyperbolic space and applications to fast diffusion flows
  (with M. Bhakta, D. Karmakar, S. Mazumdar)
  Calculus of Variations and Partial Differential Equations 64 (2025), Article 23.

• •Global compactness result and multiplicity of solutions for a class of critical exponent problems in the hyperbolic space
  (with M. Bhakta, D. Gupta, A. Sahoo)
  Communications in Contemporary Mathematics 27 (2025), no. 7, Paper No. 2450045.

• Multiplicity of positive solutions for a class of nonhomogeneous elliptic equations in the hyperbolic space
  (with D. Gupta, K. Sreenadh)
  Proceedings of the Royal Society of Edinburgh: Section A 155 (2025), no. 5, 1708–1746.

•  Stochastic completeness and (L^1)-Liouville property for second-order elliptic operators
  (with Yehuda Pinchover, P. Roychowdhury)
  Discrete and Continuous Dynamical Systems – Series S 17 (2024), no. 5–6, 1672–1685.

•  On a class of elliptic equations with critical perturbations in the hyperbolic space
  (with D. Gupta, K. Sreenadh)
  Asymptotic Analysis 138 (2024), no. 4, 225–253.

•  Fractional Hardy equations with critical and supercritical exponents
  (with M. Bhakta, L. Montoro)
  Annali di Matematica Pura ed Applicata 202 (2023), no. 1, 397–430.

•  Existence and multiplicity of positive solutions of certain nonlocal scalar field equations
  (with M. Bhakta, S. Chakraborty)
  Mathematische Nachrichten 296 (2023), no. 9, 3816–3855.

•  Existence of high energy positive solutions for a class of elliptic equations in the hyperbolic space
  (with D. Gupta, K. Sreenadh)
  Journal of Geometric Analysis 33 (2023), no. 3, Paper No. 79.

•  Improved Poincaré–Hardy inequalities on certain subspaces of the Sobolev space
  (with P. Roychowdhury)
  Proceedings of the American Mathematical Society 151 (2023), no. 8, 3513–3527.

•  Non-linear heat equation on the hyperbolic space: Global existence and finite-time blow-up
  (with D. Karmakar, S. Mazumdar)
  Advances in Differential Equations 28 (2023), no. 9–10, 779–805.

•  Classification of radial solutions to ( -\Delta_g u = e^u ) on Riemannian models
  (with E. Berchio, A. Ferrero, P. Roychowdhury)
  Journal of Differential Equations 361 (2023), 417–448.

• Hardy–Rellich and second-order Poincaré identities on the hyperbolic space via Bessel pairs
  (with E. Berchio, P. Roychowdhury)
  Calculus of Variations and Partial Differential Equations 61 (2022).

•  On the first frequency of reinforced partially hinged plates
  (with E. Berchio, A. Falocchi, A. Ferrero)
  Communications in Contemporary Mathematics 23 (2021), no. 3.

•  Improved multipolar Poincaré–Hardy inequalities on Cartan–Hadamard manifolds
  (with Elvise Berchio, Gabriele Grillo)
  Annali di Matematica Pura ed Applicata 199 (2020), no. 1, 65–80.

•  Some new aspects of perturbation theory of positive solutions of second-order linear elliptic equations
  (with Yehuda Pinchover)
  Pure and Applied Functional Analysis 5 (2020), no. 2, 295–319.

•  On the equivalence of heat kernels of second-order parabolic operators
  (with Yehuda Pinchover)
  Journal d’Analyse Mathématique 140 (2020), no. 2, 549–589.

•  On some strong Poincaré inequalities on Riemannian models and their improvements
  (with E. Berchio, P. Roychowdhury)
  Journal of Mathematical Analysis and Applications 488 (2020), no. 1, 124213.

• Integral representation using Green function for fractional Hardy equations
  (with M. Bhakta, A. Biswas, L. Montoro)
  Journal of Differential Equations 269 (2020), no. 7, 5573–5594.

•  An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds
  (with Elvise Berchio, Gabriele Grillo, Yehuda Pinchover)
  Proceedings of the Royal Society of Edinburgh: Section A 150 (2020), no. 4, 1699–1736.

•  The fractional porous medium equation on the hyperbolic space
  (with E. Berchio, M. Bonforte, G. Grillo)
  Calculus of Variations and Partial Differential Equations 59 (2020), Article 36.

•  Some Liouville-type results for eigenfunctions of elliptic operators
  (with Ari Arapostathis, Anup Biswas)
  Transactions of the American Mathematical Society 371 (2019), 4377–4409.

•  On Green functions of second-order elliptic operators on Riemannian manifolds: The critical case
  (with Yehuda Pinchover)
  Journal of Functional Analysis 274 (2018), no. 9, 2700–2724.

•  Existence results for semilinear problems in the two-dimensional hyperbolic space involving critical growth
  (with Debabrata Karmakar)
  Proceedings of the Royal Society of Edinburgh: Section A 147 (2017), no. 1, 141–176.

•  Sharp Poincaré–Hardy and Poincaré–Rellich inequalities on the hyperbolic space
  (with Elvise Berchio, Gabriele Grillo)
  Journal of Functional Analysis 272 (2017), no. 4, 1661–1703.

•  Improved (L^p)-Poincaré inequalities on the hyperbolic space
  (with Elvise Berchio, Lorenzo D’Ambrosio, Gabriele Grillo)
  Nonlinear Analysis 157 (2017), 146–166.

•  Improved higher order Poincaré inequalities on the hyperbolic space via Hardy-type remainder terms
  (with Elvise Berchio)
  Communications on Pure and Applied Analysis 15 (2016), no. 5, 1871–1892.

•  Nondegeneracy of positive solutions of a semilinear elliptic problem in the hyperbolic space
  (with K. Sandeep)
  Communications in Contemporary Mathematics 17 (2015), no. 1, 1450019.

•  Sign changing solutions of the Hardy–Sobolev–Maz’ya equation
  Advances in Nonlinear Analysis 3 (2014), no. 3, 187–196.

•  Sign changing solutions of the Brezis–Nirenberg problem in the hyperbolic space
  (with K. Sandeep)
  Calculus of Variations and Partial Differential Equations 50 (2014), 69–91.

Submitted/Preprints 

• Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space, (A. Do, N. Lam, G. Lu), 2024, arXiv: 2410.21039.

• Sharp Quantitative Forms of the Hardy Inequality on Cartan--Hadamard Manifolds via Sobolev--Lorentz Embeddings, (A. Banerjee, P. Roychowdhury), 2026, arXiv: 2601.13750. 

• Logarithmic Sobolev, Poincare and Beckner inequalities on hyperbolic spaces and Riemannian Manifolds, (A. Do, N. Lam, G. Lu), 2026, arXiv: 2602.14202. 

• Quantitative stability for fractional Hardy inequalities: Rearrangement-free techniques and Emden-Fowler analysis, (A. Banerjee, V. Sahu), 2026, arXiv: 2605.15748. 

• Gromov-Hausdorff stability and rigidity of manifolds via Heisenberg-Pauli-Weyl uncertainty principle (with Debdip Ganguly and Debabrata Karmakar), 2026, arXiv: 2609.01463.