Smoothing q-convex functions and vanishing theorems.
Smoothing q-Convex Functions in the Singular Case.
Solution of the ?-Equation with Uniform Estimates on Strictly q-Convex Domains with Non-Smooth Boundary.
Solution of the -equation on non-smooth strictly -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem
Some applications of a new integral formula for
Let M be a smooth q-concave CR submanifold of codimension k in . We solve locally the -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the -operator on (0,q)-forms in the same spaces. We also obtain estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin extension...
Some convexity properties of morphisms of complex spaces.
Some properties of positive line bundles on 1-convex complex analytic spaces
Strongly Plurisubharmonic Exhaustion Functions on 1-Convex Spaces.
Successioni crescenti di -coppie di runge di varietà analitiche complesse