By Matthias Heymann

Presenting a examine of geometric motion functionals (i.e., non-negative functionals at the area of unparameterized orientated rectifiable curves), this monograph focuses on the subclass of these functionals whose neighborhood motion is a degenerate form of Finsler metric which can vanish in sure instructions, taking into consideration curves with confident Euclidean size yet with 0 action. For such functionals, standards are constructed below which there exists a minimal motion curve top from one given set to a different. Then the homes of this curve are studied, and the non-existence of minimizers is proven in a few settings.

Applied to a geometrical reformulation of the quasipotential of Wentzell-Freidlin idea (a subfield of huge deviation theory), those effects can yield the life and homes of extreme chance transition curves among metastable states in a stochastic approach with small noise.

The publication assumes purely common wisdom in graduate-level research; all higher-level mathematical thoughts are brought alongside the way.