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Ellipsoidal Harmonics by George Dassios

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12Applications to geometry

In many real-life problems one needs to perturb some geometrical characteristics of the fundamental domain and investigate the effects of this disturbance on the actual solution of the problem. One such case appears when we disturb the boundary of the fundamental domain [85]. This is especially important for free boundary value problems, where the evolution of the boundary is part of the solution we seek, and we are interested in the stability of this evolution. In almost all these cases, it is the instantaneous local geometry that guides the evolution of the boundary. Therefore, it is imperative to know how an arbitrary perturbation affects the local geometrical characteristics of the boundary. In what follows, we ...

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