Minimum action curves in degenerate Finsler metrics : existence and properties / Matthias Heymann

• Autore: Heymann, Matthias
• Pubblicazione: Cham [Switzerland] : Springer, c2015
• Descrizione fisica: xv, 184 p. : ill. (some color) ; 24 cm
• Disciplina: 516.375
• Soggetto topico: Finsler spaces
• Classificazione: AMS 49-02; AMS 49J45; AMS 53C60; AMS 60F10; LC QA689.H49
• Nota di bibliografia: Includes bibliographical references and index
• Sommario/riassunto: Presenting a study of geometric action functionals (i.e., non-negative functionals on the space of unparameterized oriented rectifiable curves), this monograph focuses on the subclass of those functionals whose local action is a degenerate type of Finsler metric that may vanish in certain directions, allowing for curves with positive Euclidean length but with zero action. For such functionals, criteria are developed under which there exists a minimum action curve leading from one given set to another. Then the properties of this curve are studied, and the non-existence of minimizers is established in some settings. Applied to a geometric reformulation of the quasipotential of Wentzell-Freidlin theory (a subfield of large deviation theory), these results can yield the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise. The book assumes only standard knowledge in graduate-level analysis; all higher-level mathematical concepts are introduced along the way.
• ISBN: 9783319177526
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 991002949679707536
• Lo trovi qui: Univ. del Salento
• Serie: Lecture notes in mathematics, 0075-8434 ; 2134