Banach space valued Cauchy-Riemann equations with totally real boundary conditions
| dc.creator | Wehrheim, Katrin | |
| dc.date | 2004-01-27 | |
| dc.date.accessioned | 2026-07-07T05:04:54Z | |
| dc.date.available | 2026-07-07T05:04:54Z | |
| dc.description | The main purpose of this paper is to give a general regularity result for Cauchy-Riemann equations in complex Banach spaces with totally real boundary conditions. The usual elliptic $L^p$-regularity results hold true under one crucial assumption: The totally real submanifold has to be modelled on an $L^p$-space or a closed subspace thereof. Secondly, we describe a class of examples of such totally real submanifolds, namely gauge invariant Lagrangian submanifolds in the space of connections over a Riemann surface. These pose natural boundary conditions for the anti-self-duality equation on 4-manifolds with a boundary space-time splitting, leading towards the definition of a Floer homology for 3-manifolds with boundary, which is the first step in a program by Salamon for the proof of the Atiyah-Floer conjecture. The principal part of such a boundary value problem is an example of a Banach space valued Cauchy-Riemann equation with totally real boundary condition. | |
| dc.description | 35 pages. This has bubbled off from an earlier preprint (Anti-self-dual instantons with Lagrangian boundary conditions I: Elliptic theory) | |
| dc.identifier | https://arxiv.org/abs/math/0401376 | |
| dc.identifier | http://arxiv.org/abs/math/0401376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69988 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Symplectic Geometry | |
| dc.subject | 35J65; 53D12, 58B99 | |
| dc.title | Banach space valued Cauchy-Riemann equations with totally real boundary conditions | |
| dc.type | text |