Higher order fundamental forms of a surface and their applications to wave propagation and generalized derivatives

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We present a general theory of moving and deforming wave fronts by first defining and discussing the higher order fundamental forms for such a surface. These fundamental forms are then used to find the general formula for the jump of the Nth order differential of generalized functions which are discontinuous across this surface. Subsequently, we consider the wave fronts which carry multilayers and develop the theory of the generalized derivatives of the multilayers. In the process we find many new results in the theories of differential geometry and generalized functions. © 1987 Springer.

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Rendiconti del Circolo Matematico di Palermo

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