In this paper we study codimension one holomorphic foliations leaving invariant real analytic hypersurfaces. In particular, we prove that a germ of real analytic Levi-flat hypersurface with sufficiently “small” singular set is given by the zeroes of the imaginary part of a holomorphic function.

In this paper we prove the following kind of the unique continuation property. That is the zero on each geodesic of the solution in a real analytic hypersurface for second order anisotropic hyperbolic system with real analytic coefficients can be continued along this curve.

We prove the non-existence of real analytic Levi flat hypersurface whose complement is 1-convex and foliation transversely affine in a compact Kähler surface.

In this paper we apply for the rst time a new method for multivariate equation solving which was developed in for complex root determination to the real case Our main result concerns the problem of nding at least one representative point for each connected component of a real compact and smooth hypersurface The basic algorithm of yields a new method for symbolically solv ing zero dimensional po...

In this paper we study curvature properties of semi - symmetric type of totally umbilical radical transversal lightlike hypersurfaces $(M,g)$ and $(M,widetilde g)$ of a K"ahler-Norden manifold $(overline M,overline J,overline g,overline { widetilde g})$ of constant totally real sectional curvatures $overline nu$ and $overline {widetilde nu}$ ($g$ and $widetilde g$ are the induced metrics on $M$...

Let V be a complex algebraic hypersurface de ned by a polynomial f with Newton polytope ∆. It is well known that the spine of its amoeba has a structure of a tropical hypersurface. We prove in this paper that there exists a complex tropical hypersurface V∞, f such that its coamoeba is homeomorphic to the closure in the real torus of the coamoeba of V . Moreover, the coamoeba of V∞, f contains a...