Author

Mayukh Mukherjee

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Preprint Oct 2026

Cohomology and multiplicative gaps for quasi-isometries of nilpotent groups

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 multiplicative constant at least $1+\varepsilon$, for one fixed $\varepsilon>0$. We use a convex invariant of a fixed quasi-isometry $\Psi:N\to M$. The...

Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar · 0 citations

Preprint Aug 2026

Wavelength-scale optional stopping, critical Feynman-Kac gauges, and capacitary spectral inequalities

We develop two Brownian stopping methods: one uses hitting probabilities and capacity, the other moments of weighted exit distributions. On a closed $m$-dimensional Riemannian manifold, $m\geq 2$, the first gives low-energy spectral inequalities for equilibrium measures supported on sets of zero volume. Combining scale...

Mayukh Mukherjee · 0 citations