Hele-Shaw flow on hyperbolic surfaces
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/339965
- author
- Hedenmalm, Håkan LU and Shimorin, Serguei LU
- organization
- publishing date
- 2002
- 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
- 2016-04-01 16:02:49
- date last changed
- 2022-03-22 07:59:44
@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}}, 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}}, }