LEADER 01095nam 2200385 450 001 9910155690503321 005 20230808200912.0 010 $a1-5040-4258-1 035 $a(CKB)3710000000976632 035 $a(MiAaPQ)EBC4769658 035 $a(EXLCZ)993710000000976632 100 $a20170111h20161957 uy 1 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 14$aThe albatross /$fCharlotte Armstrong ; cover design by Jason Gabbert 210 1$aNew York, New York :$cMysteriousPress.com :$cOpen Road Integrated Media,$d2016. 210 4$dİ1957 215 $a1 online resource (80 pages) 311 $a0-425-02314-1 606 $aWomen spies$zGreat Britain$vFiction 607 $aGreat Britain$vFiction 615 0$aWomen spies 676 $a823.914 700 $aArmstrong$b Charlotte$0438742 702 $aGabbert$b Jason 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910155690503321 996 $aThe albatross$93409952 997 $aUNINA LEADER 04593nam 22006013 450 001 9910965974603321 005 20251116135918.0 010 $a9781470470203 010 $a1470470209 035 $a(MiAaPQ)EBC6939729 035 $a(Au-PeEL)EBL6939729 035 $a(CKB)21420569700041 035 $a(OCoLC)1321796883 035 $a(EXLCZ)9921420569700041 100 $a20220327d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIsoperimetric Inequalities in Unbounded Convex Bodies 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (100 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.276 311 08$aPrint version: Leonardi, Gian Paolo Isoperimetric Inequalities in Unbounded Convex Bodies Providence : American Mathematical Society,c2022 9781470451189 327 $aCover -- Title page -- List of symbols -- Chapter 1. Introduction -- 1.1. Historical background -- 1.2. Outline of contents -- Chapter 2. Convex bodies and finite perimeter sets -- 2.1. Convex bodies and local convergence in Hausdorff distance -- 2.2. Finite perimeter sets and isoperimetric profile -- Chapter 3. Unbounded convex bodies of uniform geometry -- 3.1. Asymptotic cylinders -- 3.2. Convex bodies of uniform geometry -- 3.3. Density estimates and a concentration lemma -- 3.4. Examples -- Chapter 4. A generalized existence result -- 4.1. Preliminary results -- 4.2. The main result -- Chapter 5. Concavity of the isoperimetric profile -- 5.1. Continuity of the isoperimetric profile -- 5.2. Approximation by smooth sets -- 5.3. Concavity of the isoperimetric profile -- Chapter 6. Sharp isoperimetric inequalities and isoperimetric rigidity -- 6.1. Convex bodies with non-degenerate asymptotic cone -- 6.2. The isoperimetric profile for small volumes -- 6.3. Isoperimetric rigidity -- Chapter 7. Asymptotic behavior of the isoperimetric profile of an unbounded convex body -- 7.1. An asymptotic isoperimetric inequality -- 7.2. Estimates on the volume growth of balls -- 7.3. Examples -- Bibliography -- Back Cover. 330 $a"We consider the problem of minimizing the relative perimeter under a volume constraint in an unbounded convex body C Rn, without assuming any further regularity on the boundary of C. Motivated by an example of an unbounded convex body with null isoperimetric profile, we introduce the concept of unbounded convex body with uniform geometry. We then provide a handy characterization of the uniform geometry property and, by exploiting the notion of asymptotic cylinder of C, we prove existence of isoperimetric regions in a generalized sense. By an approximation argument we show the strict concavity of the isoperimetric profile and, consequently, the connectedness of generalized isoperimetric regions. We also focus on the cases of small as well as of large volumes; in particular we show existence of isoperimetric regions with sufficiently large volumes, for special classes of unbounded convex bodies. We finally address some questions about isoperimetric rigidity and analyze the asymptotic behavior of the isoperimetric profile in connection with the notion of isoperimetric dimension"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aConvex bodies 606 $aBoundary value problems 606 $aIsoperimetric inequalities 606 $aCalculus of variations and optimal control; optimization -- Manifolds -- Optimization of shapes other than minimal surfaces$2msc 606 $aConvex and discrete geometry -- General convexity -- Inequalities and extremum problems$2msc 615 0$aConvex bodies. 615 0$aBoundary value problems. 615 0$aIsoperimetric inequalities. 615 7$aCalculus of variations and optimal control; optimization -- Manifolds -- Optimization of shapes other than minimal surfaces. 615 7$aConvex and discrete geometry -- General convexity -- Inequalities and extremum problems. 676 $a516/.08 676 $a516.08 686 $a49Q10$a52A40$2msc 700 $aLeonardi$b Gian Paolo$01800985 701 $aRitore?$b Manuel$00 701 $aVernadakis$b Efstratios$01800986 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910965974603321 996 $aIsoperimetric Inequalities in Unbounded Convex Bodies$94345999 997 $aUNINA