scholarly journals A sharp relative isoperimetric inequality for the square

2021 ◽  
Vol 359 (9) ◽  
pp. 1191-1199
Author(s):  
Haim Brezis ◽  
Alfred Bruckstein
Keyword(s):  
Isoperimetric Inequality ◽  
Relative Isoperimetric Inequality

scholarly journals The double cover relative to a convex domain and the relative isoperimetric inequality

2006 ◽  
Vol 80 (3) ◽  
pp. 375-382 ◽  
Author(s):  
Jaigyoung Choe
Keyword(s):  
Riemannian Manifold ◽  
Sectional Curvature ◽  
Isoperimetric Inequality ◽  
Convex Domain ◽  
Double Cover ◽  
Nonpositive Sectional Curvature ◽  
Relative Isoperimetric Inequality ◽  
Simply Connected

AbstractWe prove that a domain Ω in the exterior of a convex domain C in a four-dimensional simply connected Riemannian manifold of nonpositive sectional curvature satisfies the relative isoperimetric inequality 64π2 Vol(Ω)3 < Vol(∂Ω ~ ∂C)4. Equality holds if and only if Ω is an Euclidean half ball and ∂Ω ~ ∂C is a hemisphere.

The relative isoperimetric inequality outside convex domains in R n

2007 ◽  
Vol 29 (4) ◽  
pp. 421-429 ◽  
Author(s):  
Jaigyoung Choe ◽  
Mohammad Ghomi ◽  
Manuel Ritoré
Keyword(s):  
Isoperimetric Inequality ◽  
Convex Domains ◽  
Relative Isoperimetric Inequality
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