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Hele-Shaw flow on hyperbolic surfaces

Hedenmalm, Håkan LU and Shimorin, Serguei LU (2002) In Journal des Mathématiques Pures et Appliquées 81(3). p.187-222
Abstract
Consider a complete simply connected hyperbolic surface. The classical Hadamard theorem asserts that at each point of the surface, the exponential mapping from the tangent plane to the surface defines a global diffeomorphism. This can be interpreted as a statement relating the metric flow on the tangent plane with that of the surface. We find an analogue of Hadamard's theorem with metric flow replaced by Hele-Shaw flow, which models the injection of (two-dimensional) fluid into the surface. The Hele-Shaw flow domains are characterized implicitly by a mean value property on harmonic functions. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
exponential, hyperbolic surface, Hele-Shaw flow, mean value identifies, mapping
in
Journal des Mathématiques Pures et Appliquées
volume
81
issue
3
pages
187 - 222
publisher
Elsevier
external identifiers
  • wos:000175191900001
  • scopus:0036073932
ISSN
0021-7824
DOI
10.1016/S0021-7824(01)01222-3
language
English
LU publication?
yes
id
f04f39cc-d1d8-44db-bcaa-da058d8f6680 (old id 339965)
date added to LUP
2007-10-15 09:34:29
date last changed
2017-11-26 03:41:56
@article{f04f39cc-d1d8-44db-bcaa-da058d8f6680,
  abstract     = {Consider a complete simply connected hyperbolic surface. The classical Hadamard theorem asserts that at each point of the surface, the exponential mapping from the tangent plane to the surface defines a global diffeomorphism. This can be interpreted as a statement relating the metric flow on the tangent plane with that of the surface. We find an analogue of Hadamard's theorem with metric flow replaced by Hele-Shaw flow, which models the injection of (two-dimensional) fluid into the surface. The Hele-Shaw flow domains are characterized implicitly by a mean value property on harmonic functions. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.},
  author       = {Hedenmalm, Håkan and Shimorin, Serguei},
  issn         = {0021-7824},
  keyword      = {exponential,hyperbolic surface,Hele-Shaw flow,mean value identifies,mapping},
  language     = {eng},
  number       = {3},
  pages        = {187--222},
  publisher    = {Elsevier},
  series       = {Journal des Mathématiques Pures et Appliquées},
  title        = {Hele-Shaw flow on hyperbolic surfaces},
  url          = {http://dx.doi.org/10.1016/S0021-7824(01)01222-3},
  volume       = {81},
  year         = {2002},
}