ar X iv : m at h / 04 06 36 8 v 1 [ m at h . A P ] 1 8 Ju n 20 04 Hele - Shaw flow on weakly hyperbolic surfaces
نویسنده
چکیده
We consider the Hele-Shaw flow that arises from injection of twodimensional fluid into a point of a curved surface. The resulting fluid domains have and are more or less determined implicitly by a mean value property for harmonic functions. We improve on the results of Hedenmalm and Shimorin [8] and obtain essentially the same conclusions while imposing a weaker curvature condition on the surface. Incidentally, the curvature condition is the same as the one that appears in Hedenmalm and Perdomo’s paper [7], where the problem of finding smooth area minimizing surfaces for a given curvature form under a natural normalizing condition was considered. Probably there are deep reasons behind this coincidence.
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