https://neckpinch.com/authors/franciele-conrado/New arXiv papers by Franciele Conrado, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2605.23199arxiv:2605.23199Fri, 22 May 2026 00:00:00 GMTXu Cheng, Franciele Conrado, Neilha Pinheiro, Detang Zhou — Let (M, g, f, τ) be a complete Ricci shrinker satisfying Ric+∇²f=g/2τ and let R denote its scalar curvature. For a confined function V on M, we obtain a lower bound for the lowest eigenvalue of the Schrödinger operator −Δ+R/4+V, expressed in terms of an integral quantity involving V and the shrinker entropy, and the equality case is characterized by the potential functions. We further generalize this estimate to complete Riemannian manifolds via Perelman's μ-functional. We also study the drifted Schrödinger operator −Δ_f+V on smooth metric measure spaces. In particular, on Ricci shrinkers, we derive a lower bound for its lowest eigenvalue, with equality if and only if V is affine.Ricci solitonsScalar curvatureLimit spaces & RCDEigenvalues & spectrum https://arxiv.org/abs/2505.03499arxiv:2505.03499Tue, 06 May 2025 00:00:00 GMTFranciele Conrado, Detang Zhou — In this paper, we study the drifted Laplacian Δ_f on a hypersurface M in a Ricci shrinker (M,g,f). We prove that the spectrum of Δ_f is discrete for immersed hypersurfaces with bounded weighted mean curvature in a Ricci shrinker with a mild condition on the potential function. Next, we give a lower bound for the first nonzero eigenvalue of Δ_f when the hypersurface is an embedded f-minimal one. This estimate contains the case of compact minimal hypersurfaces in a positive Einstein manifold, in particular Choi and Wang's estimate for minimal hypersurfaces in a round sphere. The estimate also recovers the ones of Ding-Xin and Brendle-Tsiamis on self-shrinkers.Ricci solitonsEinstein metricsSelf-shrinkers & translatorsEigenvalues & spectrumMinimal & CMC surfaces https://arxiv.org/abs/2309.16017arxiv:2309.16017Wed, 27 Sep 2023 00:00:00 GMTFranciele Conrado, Detang Zhou — Let (Mⁿ,g,f) be a Ricci shrinker such that Ric_f=1/2g and the measure induced by the weighted volume element (4π)^(−n/2)e^(−f)dv_g is a probability measure. Given a point p∈ M, we consider two probability measures defined in the tangent space TₚM, namely the Gaussian measure γ and the measure overlineν induced by the exponential map of M to p. In this paper, we prove a result that provides an upper estimate for the Wasserstein distance with respect to the Euclidean metric g₀ between the measures overlineν and γ, and which also elucidates the rigidity implications resulting from this estimate.Ricci solitonsStability & uniqueness