Some isoperimetric inequalities in the plane with radial power weights

2021/04/05 by McGillivray, I · 1 citation
#49K20 #49Q20 #51M16 #53A10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.01961

Abstract

We consider the punctured plane with volume density |x|^α and perimeter density |x|^β. We show that centred balls are uniquely isoperimetric for indices (α,β) which satisfy the conditions α-β+1>0, α≤ 2β and α(β+1)≤β² except in the case α=β=0 which corresponds to the classical isoperimetric inequality.

Cited by

• Isoperimetric Bounds for Weighted Steklov Eigenvalues with Radial Weights

Related

• On The Quantitative Isoperimetric Inequality In The Plane
• Balls Isoperimetric in ℝⁿ with Volume and Perimeter Densities r^m and r^k
• On the isoperimetric problem with perimeter density r^p
• Isoperimetric Inequalities in Normed Planes
• Euclidean balls solve some isoperimetric problems with nonradial weights