Monideep Ghosh receives “Honourable Mention” for his PhD thesis
Monideep Ghosh receives “Honourable Mention” for his PhD thesis
Monideep Ghosh has received honorable mention for his thesis titled
Quantitative Stability and Perturbation Effects in Conformal PDEs and Inequalities
from the TIFR Alumni Association (TAA) as part of the TAA-Harish Chandra Memorial Awards in Mathematics for 2026. The citation from the award committee states
For significant contributions to stability problems in geometric analysis and calculus of variations
About the thesis work
Sharp functional inequalities and their quantitative stability lie at the interface of nonlinear partial differential equations, the calculus of variations, and geometric analysis. Fundamental questions include the determination of optimal constants, the characterisation of extremisers, and understanding how the deficit in an inequality quantitatively controls the distance of a function from its associated family of extremisers.
In his PhD thesis, Dr. Monideep Ghosh investigates these themes through three interrelated problems in nonlinear analysis. The first concerns the conformally invariant Chang–Gui inequality on the two-dimensional sphere, for which he establishes a quantitative stability estimate, while also recovering the characterisation of the family of extremisers in terms of conformal maps. The second addresses the attainability of the optimal constant in the Bianchi–Egnell stability inequality associated with the Hardy–Sobolev inequality, and determines conditions under which this constant is attained. The third concerns a logarithmically perturbed Brézis–Nirenberg problem on hyperbolic space, where he identifies the sharp threshold separating the existence and non-existence of positive solutions.
His work combines ideas from variational methods, concentration–compactness, conformal geometry, and asymptotic analysis to address these questions.
