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arXiv · 1004.4873

Existence and Properties of Minimum Action Curves for Degenerate Finsler Metrics

Matthias Heymann
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Abstract

I study a class of action functionals on the space of unparameterized oriented rectifiable curves in R^n. The local action is a degenerate type of Finsler metric that may vanish in certain directions, thus allowing for curves with positive Euclidean length but zero action. Given two sets A_1 and A_2, I develop criteria under which there exists a minimum action curve leading from A_1 to A_2. I then study the properties of these minimizers, and I prove the non-existence of minimizers in some situations. Applied to a geometric reformulation of the quasipotential of large deviation theory, my results can prove the existence and properties of maximum likelihood transition curves between two metastable states in a stochastic process with small noise.

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Matthias Heymann. 2010-04-27. Existence and Properties of Minimum Action Curves for Degenerate Finsler Metrics. https://arxiv.org/abs/1004.4873

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