Minimum action curves in degenerate Finsler metrics : existence and properties

Bibliographic Information

Minimum action curves in degenerate Finsler metrics : existence and properties

Matthias Heymann

(Lecture notes in mathematics, 2134)

Springer, c2015

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Note

Includes bibliographical references (p. 181-182) and index

Description and Table of Contents

Description

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.

Table of Contents

Preface.- Acknowledgements.- Acronyms.- Part I: Results.- Introduction.- Geometric Action Functionals.- Existence of Minimum Action Curves.- Properties of Minimum Action Curves.- Conclusions.- Some Proofs and Remarks.- Part II: Proofs.- Finding Points with Local Minimizers.- Proof of Lemma 6.1.- Part III: Proof of a Technical Lemma.- Proof of Lemma 6.15: Main Arguments.- Proof of Lemma 6.15: Some Technical Details.- Glossary.- Index.- References.

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Details

  • NCID
    BB19212275
  • ISBN
    • 9783319177526
  • LCCN
    2015942507
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xv, 184 p.
  • Size
    24 cm
  • Parent Bibliography ID
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