Implicit quasilinear differential systems: A geometrical approach.
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Integrable system of the heat kernel associated with logarithmic potentials
Kazuhiko Aomoto (2000)
Annales Polonici Mathematici
The heat kernel of a Sturm-Liouville operator with logarithmic potential can be described by using the Wiener integral associated with a real hyperplane arrangement. The heat kernel satisfies an infinite-dimensional analog of the Gauss-Manin connection (integrable system), generalizing a variational formula of Schläfli for the volume of a simplex in the space of constant curvature.
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