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Article overview
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Hele-Shaw flow on weakly hyperbolic surfaces | Haakan Hedenmalm
; Anders Olofsson
; | Date: |
18 Jun 2004 | Subject: | Analysis of PDEs; Differential Geometry MSC-class: 35R35;31A05; 31C12; 53B20; 76D27 | math.AP math.DG | Abstract: | We consider the Hele-Shaw flow that arises from injection of two-dimensional 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 cite{HS} 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 a recent paper of Hedenmalm and Perdomo, 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. | Source: | arXiv, math.AP/0406368 | Services: | Forum | Review | PDF | Favorites |
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