The Hele-Shaw flow and moduli of holomorphic discs
We present a new connection between the Hele-Shaw flow, also known as two-dimensional Laplacian growth, and the theory of holomorphic discs with boundary contained in a totally real submanifold. Using this, we prove short-time existence and uniqueness of the Hele-Shaw flow with varying permeability...
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| Veröffentlicht in: | Compositio mathematica 2015-12, Vol.151 (12), p.2301-2328 |
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| container_title | Compositio mathematica |
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| creator | Ross, Julius Nyström, David Witt |
| description | We present a new connection between the Hele-Shaw flow, also known as two-dimensional Laplacian growth, and the theory of holomorphic discs with boundary contained in a totally real submanifold. Using this, we prove short-time existence and uniqueness of the Hele-Shaw flow with varying permeability both when starting from a single point and also when starting from a smooth Jordan domain. Applying the same ideas, we prove that the moduli space of smooth quadrature domains is a smooth manifold whose dimension we also calculate, and we give a local existence theorem for the inverse potential problem in the plane. |
| doi_str_mv | 10.1112/S0010437X15007526 |
| format | Article |
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| fulltext | fulltext |
| identifier | ISSN: 0010-437X |
| ispartof | Compositio mathematica, 2015-12, Vol.151 (12), p.2301-2328 |
| issn | 0010-437X 1570-5846 |
| language | eng |
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| source | EZB-FREE-00999 freely available EZB journals; Cambridge University Press Journals Complete |
| subjects | Boundaries Discs Inverse Manifolds (mathematics) Mathematical analysis Mathematics Quadratures Theoretical mathematics Uniqueness |
| title | The Hele-Shaw flow and moduli of holomorphic discs |
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