TL;DR
This paper evaluates functional determinants of the scalar Laplacian on various geometries with boundary conditions using conformal techniques, analyzing boundary effects and contributions in different dimensions.
Contribution
It provides new explicit calculations of functional determinants on complex geometries with boundary effects in multiple dimensions.
Findings
Explicit formulas for determinants on spherical caps and slices
Analysis of boundary effects and non-smooth boundary contributions
Edge and vertex contributions to the heat kernel coefficient
Abstract
Functional determinants for the scalar Laplacian on spherical caps and slices, flat balls, shells and generalised cylinders are evaluated in two, three and four dimensions using conformal techniques. Both Dirichlet and Robin boundary conditions are allowed for. Some effects of non-smooth boundaries are discussed; in particular the 3-hemiball and the 3-hemishell are considered. The edge and vertex contributions to the coefficient are examined.
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