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Creators/Authors contains: "Glaudo, Federico"

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  1. ; ; (, Communications in Partial Differential Equations)
    Free, publicly-accessible full text available August 3, 2026
  2. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    Abstract For every d ≥ 3 d\geq 3, we construct a noncompact smooth 𝑑-dimensional Riemannian manifold with strictly positive sectional curvature without isoperimetric sets for any volume below 1.We construct a similar example also for the relative isoperimetric problem in (unbounded) convex sets in R d \mathbb{R}^{d}.The examples we construct have nondegenerate asymptotic cone.The dimensional constraint d ≥ 3 d\geq 3is sharp.Our examples exhibit nonexistence of isoperimetric sets only for small volumes; indeed, in nonnegatively curved spaces with nondegenerate asymptotic cones, isoperimetric sets with large volumes always exist.This is the first instance of noncollapsed nonnegatively curved space without isoperimetric sets. 
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  3. (, Mathematische Annalen)
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