7 papers
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…
Linear-growth harmonic functions for nonsymmetric random walks on groups of polynomial growth
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
Let be a finitely generated group of polynomial growth and let be an adapted, Abelian-centered probability measure with a finite exponential moment (not necessarily symmetr…
Exact versus monotone isoperimetric profiles of finitely generated groups
Mayukh Mukherjee
Gromov asked whether the exact isoperimetric profile of an infinite finitely generated group is comparable, at the same cardinality, to its greatest nondecreasing minorant. We comp…
Green geometry, Martin boundary and random walk asymptotics on groups
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
We identify a single computationally checkable analytic quantity interlacing Martin boundary collapse, Green geometry, and linear escape for transient random walks on finitely gene…