LEADER 04761nam 22006255 450 001 9910918598903321 005 20250807143302.0 010 $a9789819769841 010 $a9819769841 024 7 $a10.1007/978-981-97-6984-1 035 $a(CKB)37054832600041 035 $a(MiAaPQ)EBC31852191 035 $a(Au-PeEL)EBL31852191 035 $a(DE-He213)978-981-97-6984-1 035 $a(OCoLC)1484072488 035 $a(EXLCZ)9937054832600041 100 $a20241219d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAnisotropic Isoperimetric Problems and Related Topics /$fedited by Valentina Franceschi, Alessandra Pluda, Giorgio Saracco 205 $a1st ed. 2024. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2024. 215 $a1 online resource (216 pages) 225 1 $aSpringer INdAM Series,$x2281-5198 ;$v62 311 08$a9789819769834 311 08$a9819769833 327 $a -- Geometric invariants of non-smooth framed curves (by Bevilacqua, Lussardi, and Marzocchi) -- Minimal periodic foams with equal cells (by Cesaroni and Novaga) -- On a Cheeger--Kohler-Jobin inequality (by Lucardesi, Mazzoleni, and Ruffini) -- Isoperimetry on manifolds with Ricci bounded below: overview of recent results and methods (by Pozzetta) -- Stochastic homogenization of functionals defined on finite partitions (by Bach and Ruf) -- On sets with finite distributional fractional perimeter (by Comi and Stefani) -- On a Free-Endpoint Isoperimetric Problem in R^2 (by Alama, Bronsard, and Vriend) -- Isoperimetric sets in nonnegative scalar curvature and their role through various concepts of mass (by Benatti and Fogagnolo) -- A crystallization result in two dimensions for a soft disc affine potential (by Del Nin and De Luca). 330 $aThis book contains contributions from speakers at the "Anisotropic Isoperimetric Problems & Related Topics" conference in Rome, held from Sep 5 to 9, 2022. The classic isoperimetric problem has fascinated mathematicians of all eras, starting from the ancient Greeks, due to its simple statement: what are the sets of a given volume with minimal perimeter? The problem is mathematically well understood, and it plays a crucial role in explaining physical phenomena such as soap bubble shapes. Variations of the problem, including weighted counterparts with density dependencies, representing inhomogeneity and anisotropy of the medium, broaden its applicability, even in non-Euclidean environments, and they allow for descriptions, e.g., of crystal shapes. At large, the perimeter's physical interpretation is that of an attractive force; hence, it also appears in describing systems of particles where a balance between attractive and repulsive forces appears. A prominent example is that of Gamow's liquid drop model for atomic nuclei, where protons are subject to the strong nuclear attractive force (represented by the perimeter) and the electromagnetic repulsive force (represented by a nonlocal term). Such a model has been shown to be sound, as it explains the basic characteristics of the nuclei, and it successfully predicts nuclear fission for nuclei with a large atomic number. Similar energy functionals model various physical and biological systems, showcasing the competition between short-range interfacial and long-range nonlocal terms, leading to pattern formation. The authors mention, e.g., the Ohta?Kawasaki model for microphase separation of diblock copolymers and the Yukawa potential for colloidal systems. Despite diverse systems, the emergence of microphases follows similar patterns, although rigorously proving this phenomenon remains a challenge. The book collects several contributions within these topics, shedding light on the current state of the art. 410 0$aSpringer INdAM Series,$x2281-5198 ;$v62 606 $aMathematics 606 $aMathematical analysis 606 $aDiscrete mathematics 606 $aApplications of Mathematics 606 $aAnalysis 606 $aApplications of Discrete Mathematics 615 0$aMathematics. 615 0$aMathematical analysis. 615 0$aDiscrete mathematics. 615 14$aApplications of Mathematics. 615 24$aAnalysis. 615 24$aApplications of Discrete Mathematics. 676 $a519 700 $aFranceschi$b Valentina$01781095 701 $aPluda$b Alessandra$01781096 701 $aSaracco$b Giorgio$01781097 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910918598903321 996 $aAnisotropic Isoperimetric Problems and Related Topics$94305888 997 $aUNINA