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math.CA2026
A sharp covering theorem and Solyanik estimates for Euclidean balls
Mayukh Mukherjee
For every finite family of Euclidean balls in , , and every , we select a subfamily whose -dilations cover the original union and whose undilat…
math.GR2026
Spectral Dehn functions and a characterisation of word-hyperbolicity
Mayukh Mukherjee
We introduce a \emph{spectral Dehn function} \[ Λ_{\mathcal{P}}(n):=\inf λ_1(Δ), \] where is the first Dirichlet eigenvalue of the random-walk Laplacian on a van Kampen di…
math.SP2026
An Approximate Inverse Spectral Theorem for Manifolds of Constant Negative Curvature
Mayukh Mukherjee
A classical theorem of Colin de Verdière shows that on a closed manifold of fixed topology one can prescribe an arbitrary finite portion of the Laplace-Beltrami spectrum (including…