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Aditya Tiwari

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Preprint Sep 2026

Minimizers of Laplace eigenvalues under a lower curvature bound

We prove a sharp comparison, with Obata-type rigidity, for all Neumann eigenvalues of one-dimensional $\mathrm{CD}(1,2)$ spaces against the Legendre model, under a convexity condition on the density. It follows that minimizers of the $k$-th Laplace eigenvalue among closed surfaces of Gaussian curvature at least $1$ can...

Aditya Tiwari · 0 citations

Preprint Aug 2026

A Weighted Discretization of Riemannian Manifolds with Lower Ricci Bounds

Let $(M,g)$ be a connected, compact, $n$-dimensional Riemannian manifold with $\operatorname{Ric}(M,g)\geq-(n-1)\kappa g$. We introduce a weighted combinatorial Laplacian on $\varepsilon$-discretizations of $M$ and prove a spectral comparison theorem between the weighted graph Laplacian and the Laplace-Beltrami operato...

Aditya Tiwari · 0 citations