The Cheeger constant of curved tubes

DOI10.1007/s00013-018-1282-xzbMath1415.49027arXiv1811.12095OpenAlexW2902948419WikidataQ128537528 ScholiaQ128537528MaRDI QIDQ1737366

Petr Vlachopulos, David Krejčiřík, Gian Paolo Leonardi

Publication date: 27 March 2019

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.12095

zbMATH Keywords

Cheeger constantspherical shellsCheeger setcurved tubestubular neighbourhoods of curves

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Optimization of shapes other than minimal surfaces (49Q10) Inequalities and extremum problems in real or complex geometry (51M16)

Related Items (max. 100)

On the Cheeger problem for rotationally invariant domains ⋮ Isoperimetric sets and \(p\)-Cheeger sets are in bijection ⋮ Cheeger sets for rotationally symmetric planar convex bodies ⋮ Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cheeger sets in strips and non-convex domains
• Two dimensions are easier
• The Cheeger constant of curved strips
• Solutions of the Cheeger problem via torsion functions
• The total variation flow in \(\mathbb R^N\)
• The Cheeger constant of a Jordan domain without necks
• Two examples of minimal Cheeger sets in the plane
• First eigenfunctions of the 1-Laplacian are viscosity solutions
• Characterization of Cheeger sets for convex subsets of the plane
• The first eigenvalue of the Laplacian, isoperimetric constants, and the max flow min cut theorem
• Sets of Finite Perimeter and Geometric Variational Problems
• An Overview on the Cheeger Problem
• There is More than One Way to Frame a Curve
• On the strict monotonicity of the first eigenvalue of the 𝑝-Laplacian on annuli
• Functions locally almost 1-harmonic

This page was built for publication: The Cheeger constant of curved tubes