2023
DOI: 10.1007/s11854-023-0310-3
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Semiclassical analysis of a nonlocal boundary value problem related to magnitude

Heiko Gimperlein,
Magnus Goffeng,
Nikoletta Louca

Abstract: We study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using recent techniques developed for pseudodifferential boundary problems we discuss the structure of the solution operator and resulting properties of the magnitude. In a semiclassical limit we obtain an asymptotic expansion of the magnitude in terms of curvature invarian… Show more

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