Semianalyticity of isoperimetric profiles
Pierre Pansu (LM-Orsay), Renata Grimaldi (DMMM), Stefano Nardulli, (LM-Orsay, DMMM)
TL;DR
This paper proves that in dimensions less than 8, the isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic functions, revealing their structured geometric nature.
Contribution
It establishes the semi-analyticity of isoperimetric profiles for compact real analytic Riemannian manifolds in dimensions under 8, a new geometric regularity result.
Findings
Isoperimetric profiles are semi-analytic in dimensions <8.
Semi-analyticity holds for compact real analytic Riemannian manifolds.
Dimension plays a crucial role in the regularity of isoperimetric profiles.
Abstract
It is shown that, in dimensions , isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Topological and Geometric Data Analysis