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29 March 2024
 
  » arxiv » math.AP/0406368

 Article overview


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
AbstractWe 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
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