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In this note we prove in the nonlinear setting of $CD(K,infty)$ spaces the stability of the Krasnoselskii spectrum of the Laplace operator $-Delta$ under measured Gromov-Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of $CD^*(K,N)$ metric measure spaces with uniformly bounded diameter. Additionally, we show that every element $lambda$ in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial $u$ satisfying the eigenvalue equation $- Delta u = lambda u$.
We study stability of the spectral gap and observable diameter for metricmeasure spaces satisfying the RCD(1, $infty$) condition. We show that if such a space has an almost maximal spectral gap, then it almost contains a Gaussian component, and the L
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary structures from
We examine topological properties of pointed metric measure spaces $(Y, p)$ that can be realized as the pointed Gromov-Hausdorff limit of a sequence of complete, Riemannian manifolds ${(M^n_i, p_i)}_{i=1}^{infty}$ with nonnegative Ricci curvature. Ch
Consider a general nonlinear optimal control problem in finite dimension, with constant state and/or control delays. By the Pontryagin Maximum Principle, any optimal trajectory is the projection of a Pontryagin extremal. We establish that, under appr
A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we gener