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Minimum action curves in degenerate ...

Heymann, Matthias.

Minimum action curves in degenerate Finsler metricsexistence and properties /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Minimum action curves in degenerate Finsler metricsby Matthias Heymann.
Reminder of title:	existence and properties /
Author:	Heymann, Matthias.
Published:	Cham :Springer International Publishing :2015.
Description:	xv, 186 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Finsler spaces.
Online resource:	http://dx.doi.org/10.1007/978-3-319-17753-3
ISBN:	9783319177533 (electronic bk.)

Minimum action curves in degenerate Finsler metricsexistence and properties /
Heymann, Matthias.

Minimum action curves in degenerate Finsler metricsexistence and properties /[electronic resource] :by Matthias Heymann. - Cham :Springer International Publishing :2015. - xv, 186 p. :ill., digital ;24 cm. - Lecture notes in mathematics,21340075-8434 ;. - Lecture notes in mathematics ;2035..

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: 9783319177533 (electronic bk.)

Standard No.: 10.1007/978-3-319-17753-3doiSubjects--Topical Terms:

537265
Finsler spaces.

LC Class. No.: QA689 / .H49 2015

Dewey Class. No.: 516.375

Minimum action curves in degenerate Finsler metricsexistence and properties /
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490 1 $a Lecture notes in mathematics, $x 0075-8434 ; $v 2134
520 $a 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.
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