Optimal domains for the Cheeger inequality

2025/10/09 by Dorin Bucur, Bucur, Dorin, Giuseppe Buttazzo +3
Mathematics · #35J25 #35P15 #49J45 #49Q10 #49R05 #Analytic and geometric function theory #FOS: Mathematics #Holomorphic and Operator Theory #Optimization and Control (math.OC) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2510.08032

openalex publication_date 2025/10/09 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the scale invariant shape functional F_p,q(Ω)=\fracλ_p^1/p(Ω)λ_q^1/q(Ω), where 1≤ q

Citations

• Capacitary inradius and Poincaré-Sobolev inequalities
• On a class of Cheeger inequalities
• An overview on the Cheeger problem
• Reverse Cheeger inequality for planar convex sets
• Existence of minimizers for spectral problems

Related

• On a class of Cheeger inequalities
• Optimal domains for the Cheeger inequality
• On some rescaled shape optimization problems
• Symmetry breaking in a constrained Cheeger type isoperimetric inequality
• On a Cheeger--Kohler-Jobin inequality