On the mixed Cauchy problem with data on singular conics

We consider a problem of mixed Cauchy type for certain holomorphic partial differential operators whose principal part $Q_{2p}(D)$ essentially is the (complex) Laplace operator to a power, $\Delta^p$. We pose inital data on a singular conic divisor given by P=0, where $P$ is a homogeneous polynomial of degree $2p$. We show that this problem is uniquely solvable if the polynomial $P$ is elliptic, in a certain sense, with respect to the principal part $Q_{2p}(D)$

On the existence of holomorphic embeddings of strictly pseudoconvex algebraic hypersurfaces into spheres

We show that there are strictly pseudoconvex, real algebraic hypersurfaces in \bC^{n+1} that cannot be locally embedded into a sphere in \bC^{N+1} for any $N$. In fact, we show that there are strictly pseudoconvex, real algebraic hypersurfaces in \bC^{n+1} that cannot be locally embedded into any compact, strictly pseudoconvex, real algebraic hypersurface