Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

"We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C Rn, without assuming any further regularity on the boundary of C. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of unbounded convex body with uniform geometry. We then provide a handy characterization of the uniform geometry property and, by exploiting the notion of asymptotic cylinder of C, we prove existence of isoperimetric regions in a generalized sense. By an approximation argument we show the strict concavity of the isoperimetric profile and, consequently, the connectedness of generalized isoperimetric regions. We also focus on the cases of small as well as of large volumes; in particular we show existence of isoperimetric regions with sufficiently large volumes, for special classes of unbounded convex bodies. We finally address some questions about isoperimetric rigidity and analyze the asymptotic behavior of the isoperimetric profile in connection with the notion of isoperimetric dimension"--

Convex bodies. --- Boundary value problems. --- Isoperimetric inequalities.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The study of isoperimetric inequalities involves a fascinating interplay of analysis, geometry and the theory of partial differential equations. Several conjectures have been made and while many have been resolved, a large number still remain open.One of the principal tools in the study of isoperimetric problems, especially when spherical symmetry is involved, is Schwarz symmetrization, which is also known as the spherically symmetric and decreasing rearrangement of functions. The aim of this book is to give an introduction to the theory of Schwarz symmetrization and study some of its applicat

Isoperimetric inequalities. --- Symmetry (Mathematics) --- Invariance (Mathematics) --- Group theory --- Automorphisms --- Geometry, Plane --- Inequalities (Mathematics) --- Isoperimetric inequalities

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Isoperimetric inequalities. --- Inégalités isopérimétriques --- Inégalités variationnelles

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Inequalities (Mathematics) --- Mathematical physics --- Isoperimetric inequalities --- Inégalités (Mathématiques) --- Physique mathématique --- Inégalités isopérimétriques

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Isoperimetric inequalities. --- Inégalités isopérimétriques. --- Géometrie convexe --- Géometrie intégrale --- Inégalités (mathématiques) --- Géometrie convexe --- Géometrie intégrale --- Inégalités (mathématiques) --- Inégalités isopérimétriques.