Abstract
In this paper we study the \(\overline{\partial}\)-equation with zero Cauchy data along a hypersurface with constant signature. Applications to the solvability of the tangential Cauchy–Riemann equations for smooth forms with compact support and currents on the hypersurface are given. We also prove that the Hartogs phenomenon holds in weakly 2-convex–concave hypersurfaces with constant signature of Stein manifolds.
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Brinkschulte, J. The Hartogs phenomenon in hypersurfaces with constant signature. Ann. Mat. Pura Appl. IV. Ser. 183, 515–535 (2004). https://doi.org/10.1007/s10231-004-0103-y
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DOI: https://doi.org/10.1007/s10231-004-0103-y