5 papers
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…
Sharp thresholds for the Escobar functional: the Escobar-Willmore mass, geometric selection, and compactness trichotomy
Mayukh Mukherjee, Utsab Sarkar
We study the hemisphere threshold for the conformally covariant Escobar functional on compact Riemannian manifolds with boundary. The near-threshold landscape is organize…
The Lipschitz Liouville Property, Affine Rigidity, and Coarse Harmonic Coordinates on Groups of Polynomial Growth
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
We develop a quantitative theory of Lipschitz harmonic functions (LHF) on finitely generated groups, with emphasis on the Lipschitz Liouville property, affine rigidity, and quasi-i…
Wulff Isoperimetry on Cayley Graphs: Submodular BV, Tempered Følner, and Profile Ratio Bounds
Mayukh Mukherjee
We develop a BV framework on Cayley graphs, which yields a sharp discrete Wulff isoperimetric inequality with the best constant tied to the generating set/stencil , a quantitati…
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…