Titlebook: Laplacian Growth on Branched Riemann Surfaces; Bj?rn Gustafsson,Yu-Lin Lin Book 2021 The Editor(s) (if applicable) and The Author(s), unde

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Weak Solutions and Balayage,ies for subharmonic functions, or in terms of partial balayage. Some versions of inverse balayage are also discussed, this needed as a preparatory step for constructing more general Laplacian evolutions. Finally, the exponential transform and the elimination function are introduced.

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Weak and Strong Solutions on Riemann Surfaces,mplex plane, and the somewhat abstract theory is illustrated by examples. It is also shown that the partial balayage, which represents time evolution, commutes with the covering projection in a natural sense.

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Examples,sent nonunivalent evolutions. One of these actually represents, in a certain sense, the suction case. Finally, a general discussion of injection contra suction from a Riemann surface perspective is given.

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Lecture Notes in Mathematicshttp://image.papertrans.cn/l/image/581311.jpg

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