4 papers · 1 filter
Gagliardo--Nirenberg extremals on manifolds with small holes
Mayukh Mukherjee, Utsab Sarkar
We study the sharp homogeneous Dirichlet Gagliardo--Nirenberg quotient on a closed Riemannian manifold with holes of small capacity and connected complements. For each fixed expone…
Cohomology and multiplicative gaps for quasi-isometries of nilpotent groups
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
We construct two word metrics on the same seven-dimensional torsion-free nilpotent lattice whose asymptotic cones are isometric, but for which every quasi-isometry has multiplicati…
Wavelength-scale optional stopping, critical Feynman-Kac gauges, and capacitary spectral inequalities
Mayukh Mukherjee
We develop two Brownian stopping methods: one uses hitting probabilities and capacity, the other moments of weighted exit distributions. On a closed -dimensional Riemannian mani…
Quantitative stability and strict inequalities for the Escobar functional
Mayukh Mukherjee, Utsab Sarkar
For Euclidean domains whose boundaries are sufficiently close to a sphere in , we bound the deficit of the Escobar constant from below by the squared norm of the bou…