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| The zero surface tension limit of Hele-Shaw flows (Laplacian growth) is known for many important features, including the finite-time singularities that limit the evolution (in the Cauchy-problem sense) of a large family of classical (strong) solutions. Finding an appropriate generalization of the classical problem has been the focus of many recent developments in this field. We reformulate the deformation quantization of the Poisson structure of Laplacian growth (first introduced a decade ago) and discuss the function-theoretic aspect of the associated weak solutions. Finally, using the family of deformed solutions, we derive and interpret the weak resolution of conical singularities and their geometric characteristics. |
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