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Hele-Shaw on weakly hyperbolic surfaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-4971-7147
2005 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 54, no 4, 1161-1180 p.Article in journal (Refereed) Published
Abstract [en]

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 [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.

Place, publisher, year, edition, pages
2005. Vol. 54, no 4, 1161-1180 p.
Keyword [en]
Hele-Shaw flow, biharmonic Green function, mean value property
Identifiers
URN: urn:nbn:se:kth:diva-15048ISI: 000231916400011Scopus ID: 2-s2.0-26444526262OAI: oai:DiVA.org:kth-15048DiVA: diva2:333089
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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