Abstract
We prove the existence of analytic discs with boundaries in a non- compact target manifold (M ⊂ T x ℂ2) without exceptional points. It is shown that the manifolds M in the considered class are globally foliated by the solutions of related Riemann-Hilbert problems. The proof is based on a fixed-point equation for a compact operator and utilizes uniform norm estimates for the inverses of related Toeplitz operators.
The first two authors were supported by Deutsche Forschungsgemeinschaft, grant We 1704/2-2
The third author was supported by NSF, grant DMS 9401848
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Wegert, E., Khimchiachvili, G., Spikovsky, I. (1999). On Totally Real Non-Compact Manifolds Globally Foliated by Analytic Discs. In: Begehr, H.G.W., Gilbert, R.P., Wen, GC. (eds) Partial Differential and Integral Equations. International Society for Analysis, Applications and Computation, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3276-3_7
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DOI: https://doi.org/10.1007/978-1-4613-3276-3_7
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