From the 1 of 14 linked papers with an AI index.
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Spaces of metrics with positive spectral scalar curvature
Gioacchino Antonelli, Georg Frenck, Bernhard Hanke
The paper investigates the space of Riemannian metrics on a closed manifold for which a generalized conformal Laplacian is positive, establishing homotopy equivalences and contract…
Connected sum of manifolds with spectral Ricci lower bounds
Gioacchino Antonelli, Kai Xu
Let , , and . We prove that if and are two smooth -manifolds that admit a complete Riemannian metric satisfying \[-γÎ+ \m…
New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry
Gioacchino Antonelli, Kai Xu
We show a sharp and rigid spectral generalization of the classical Bishop--Gromov volume comparison theorem: if a closed Riemannian manifold of dimension satisfies…
Rigidity and flexibility under spectral Ricci lower bounds and mean-convex boundary
Gioacchino Antonelli, Yangyang Li, Paul Sweeney
We study Riemannian manifolds with mean-convex boundary whose Ricci curvature is nonnegative in a spectral sense. Our first main result is a sharp spectral extension of a…
Positive mass and isoperimetry for continuous metrics with nonnegative scalar curvature
Gioacchino Antonelli, Mattia Fogagnolo, Stefano Nardulli +1
This paper deals with quasi-local isoperimetric versions of the positive mass theorem on -manifolds endowed with continuous complete metrics having nonnegative scalar curvature…
Isoperimetric problems and lower bounds on curvature
Gioacchino Antonelli
This note surveys some classical results and recent developments on the interplay between lower curvature bounds and the isoperimetric problem. It is based on mini-courses given at…