Short CommunicationsNo Access

SOLUTION TO AND PROBLEM FOR SMOOTH FORMS AND CURRENTS ON STRICTLY q-CONVEX DOMAINS

SAYED SABER

Mathematics Department, Faculty of Science, Beni-Suef University, Egypt

https://doi.org/10.1142/S0219887812200022Cited by:2 (Source: Crossref)

Abstract

On a strictly q-convex domain D in a Kähler manifold X, we obtain the solvability of the -problem for smooth forms and currents on boundaries of D. Moreover, we study the solvability of the -problem for extensible currents.

Keywords:

AMSC: 32W05, 32F10, 32Q15, 32W10

References

A. Boggess , CR Manifolds and the Tangential Cauchy-Riemann Complex ( CRC Press , Boca Raton, Florida , 1991 ) . Google Scholar
A. Martineau, Strasbourg RCP 25, (1966). Google Scholar
C. Laurent-Thiébaut, Int. J. Math. 16(9), 1063 (2005). Link, Web of Science, Google Scholar
J. Brinkschulte, Ark. Mat. 42, 259 (2004). Web of Science, Google Scholar
J. Brinkschulte, C. D. Hill and M. Nacinovich, Manuscripta Math. 131, 503 (2010). Web of Science, Google Scholar
J. J. Kohn and H. Rossi, Ann. of Math. 81, 451 (1965). Web of Science, Google Scholar
J. Le Potier, Math. Ann. 218, 35 (1975). Web of Science, Google Scholar
J. Michel and M.-C. Shaw, Math. Ann. 311, 147 (1998). Web of Science, Google Scholar
J. Morrow and K. Kodaira , Complex Manifolds ( Rinehart and Winston , Holt , 1971 ) . Google Scholar
J.-P. Rosay, Duke Math. J. 49, 121 (1982). Web of Science, Google Scholar
J.-P. Serre, Comment. Math. Helv. 29, 9 (1955). Google Scholar
G. M. Henkin, C. R. Acad. Sci. Paris Sér. I Math. 292(1), 27 (1981). Google Scholar
M. Nacinovich and G. Valli, Ann. Mat. Pura App. 146, 123 (1987). Web of Science, Google Scholar
O. Abdelkader, C. R. Acad. Sci. Paris, t.290, Série A 75 (1980). Google Scholar
O. Abdelkader and S. Saber, Int. J. Geom. Meth. Mod. Phys. 2(3), 467 (2005). Link, Web of Science, Google Scholar
O. Abdelkader and S. Saber, Int. J. Geom. Meth. Mod. Phys. 4(2), 1 (2007). Web of Science, Google Scholar
S. Saber, Global boundary regularity for the $\ov\partial$-problem on strictly q-convex and q-concave domains, to appear in Complex Anal. Operator Theory J . Google Scholar
S. Saber, Lobachevskii J. Math. 32, (2011). Google Scholar
S. Sambou, Math. Nachr. 235, 179 (2002). Web of Science, Google Scholar