On the Applications of Bochner-Kodaira-Morrey-Kohn Identity

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Authors: S. SABER

DOI: 10.46793/KgJMat2106.881S


This paper is devoted to studying some applications of the Bochner-Kodaira-Morrey-Kohn identity. For this study, we define a condition which is called (Hq) condition which is related to the Levi form on the complex manifold. Under the (Hq) condition and combining with the basic Bochner-Kodaira-Morrey-Kohn identity, we study the L2 Cauchy problems on domains in n, Kähler manifold and in projective space. Also, we study this problem on a piecewise smooth strongly pseudoconvex domain in a complex manifold. Furthermore, the weighted L2 Cauchy problem is studied under the same condition in a Kähler manifold with semi-positive holomorphic bisectional curvature. On the other hand, we study the global regularity and the L2 theory for the -operator with mixed boundary conditions on an annulus domain in a Stein manifold between an inner domain which satisfy (Hnq1) and an outer domain which satisfy (Hq).


, -Neumann operator, weakly q-convex domains.


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