Explicit Hodge decomposition on Riemann surfaces
We present a construction of the explicit Hodge decomposition for $\bar\partial$-equation on Riemann surfaces.
math.CV↗
arXiv subjects
Gennadi M. Henkin
Publications and source records attributed to Gennadi M. Henkin.
Explicit Hodge-type decomposition on projective complete intersections
We construct an explicit homotopy formula for the d-bar complex on a complete intersection subvariety V in CP^n. This formula can be interpreted as a Hodge-type decomposition for residual currents on V.
math.AG↗
Residual d-bar-cohomology and the complex Radon transform on subvarieties of CPn
We show that the complex Radon transform realizes an isomorphism between the space of residual $\bar\partial$-cohomologies of a locally complete intersection subvariety in a linearly concave domain of ${\C}P^n$ and the space of holomorphic solutions of the associated homogeneous system of differential equations withconstant coefficients in the dual domain in $({\C}P^n)^*$.
math.CV↗
Inversion formulas for complex Radon transform on projective varieties and boundary value problems for systems of linear PDE
Let $G\subset \C P^n$ be a linearly convex compact with smooth boundary, $D={\C}P^n\setminus G$, and let $D^* \subset (\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of dimension $d$ we construct an explicit inversion formula for the complex Radon transform $R_V:\ H^{d,d-1}(V\cap D)\to H^{1,0}(D^*)$, and explicit formulas for solutions of an appropriate boundary value problem for the corresponding system of differential equations with constant coefficients on $D^*$.
math.CV↗