Hele-Shaw on weakly hyperbolic surfaces
2005 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, Vol. 54, no 4, 1161-1180 p.Article in journal (Refereed) Published
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 are more or less determined implicitly by a mean value property for harmonic functions. We improve on the results of Hedenmalm and Shimorin  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 , 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.
Place, publisher, year, edition, pages
2005. Vol. 54, no 4, 1161-1180 p.
Hele-Shaw flow, biharmonic Green function, mean value property
IdentifiersURN: urn:nbn:se:kth:diva-15048ISI: 000231916400011ScopusID: 2-s2.0-26444526262OAI: oai:DiVA.org:kth-15048DiVA: diva2:333089
QC 201005252010-08-052010-08-05Bibliographically approved