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math.GR2025
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…
math.GR2025
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…
math.GR2024
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…