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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
and
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 Masson SAS
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
2016-04-01 16:02:49
date last changed
2025-10-14 10:46:52
@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}},
  keywords     = {{exponential; hyperbolic surface; Hele-Shaw flow; mean value identifies; mapping}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{187--222}},
  publisher    = {{Elsevier Masson SAS}},
  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}},
  doi          = {{10.1016/S0021-7824(01)01222-3}},
  volume       = {{81}},
  year         = {{2002}},
}