On the Local Character of the Solutions of an Atypical Linear Differential Equation in Three Variables and a Related Theorem for Regular Functions of Two Complex Variables

Abstract

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Laplace operators on Sasaki-Einstein manifolds

“…The tangential Cauchy-Riemann operator∂ B and the associated Kohn-Rossi cohomology groups H p,q ∂ B (S) were first introduced in [3][4][5]. Given a complex manifold with boundary, Lewy, Kohn, and Rossi considered under what circumstances functions on the boundary can be extended to holomorphic functions in the bulk.…”

SOBOLEV ESTIMATES FOR THE LOCAL EXTENSION OF BOUNDARY HOLOMORPHIC FORMS ON REAL HYPERSURFACES IN ℂn

“…The∂-closed extension problem and the local solvability of the tangential Cauchy-Riemann equation for functions were first introduced in two papers by Hans Lewy [17,18]. For the case when M is the boundary of a smoothly bounded domain Ω in C n , the global∂-closed extension problem for forms from M to the domain Ω was studied by J. J. Kohn and H. Rossi [14], who first introduced the∂ b -complex.…”

Holomorphic Extension Problem for Standard Real Submanifolds of Second Kind

“…Ever since Lewy [5] studied the holomorphic extension problem for pseudo-convex hypersurfaces in C 2 , Lewy [6] , Wells [12] , [13] , Greenfield [2] obtained many results on the hull of holomorphy of lower-dimensional real submanifolds in complex manifolds. On the other hand Tanaka [9] , [10] , [11] studied the pseudo-conformal equivalence between real submanifolds as 'an example of geometry of differential systems and at the same time he introduced in a group-theoretic manner an ideal class of real submanifolds in complex vector spaces which are called 'standard real submanifolds'.…”