By Matthias Heymann
Presenting a learn of geometric motion functionals (i.e., non-negative functionals at the house of unparameterized orientated rectifiable curves), this monograph focuses on the subclass of these functionals whose neighborhood motion is a degenerate kind of Finsler metric that could vanish in sure instructions, bearing in mind curves with confident Euclidean size yet with 0 action. For such functionals, standards are built lower than which there exists a minimal motion curve major from one given set to a different. Then the homes of this curve are studied, and the non-existence of minimizers is verified in a few settings.
Applied to a geometrical reformulation of the quasipotential of Wentzell-Freidlin conception (a subfield of enormous deviation theory), those effects can yield the life and homes of extreme probability transition curves among metastable states in a stochastic method with small noise.
The publication assumes in basic terms average wisdom in graduate-level research; all higher-level mathematical options are brought alongside the way.
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