In this paper, we consider minimal hypersurfaces in the product space Hn × R. We begin by studying examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations. We then consider minimal hypersurfaces with finite total curvature. This assumption implies that the corresponding curvature goes to zero uniformly at infinity. We show that surfaces with finite total int...

The Chern-Moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries. Extending the work of N. K. Stanton, we consider the local equivalence problem for symmetric Levi degenerate hypersurfaces of finite type in C2. The results give complete normalizations for such hypersurfaces, which respect the symmetries. In particular, they apply to tubes and rigid hy...

We present a new characterization of Cartan isoparametric hypersurfaces in terms of properties of the polynomial that determines the algebraic set of planar normal sections on the homogeneous isoparametric hypersurfaces in spheres. We show that Cartan isoparametric hypersurfaces are the only homogeneous isoparametric hypersurfaces in spheres for which the infinity Laplacian of the polynomial th...

ABSTRACT. We study those smooth complex hypersurfaces W in C having the property that all holomorphic functions of finite weighted L norm on W extend to entire functions with finite weighted L norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces W in C such that any entire function wit...

We introduce various families of irreducible homaloidal hypersurfaces in projective space Pr, for all r ≥ 3. Some of these are families of homaloidal hypersurfaces whose degrees are arbitrarily large as compared to the dimension of the ambient projective space. The existence of such a family solves a question that has naturally arisen from the consideration of the classes of homaloidal hypersur...

We prove the existence of a one parameter family of minimal embedded hypersurfaces in R, for n ≥ 3, which generalize the well known 2 dimensional ”Riemann minimal surfaces”. The hypersurfaces we obtain are complete, embedded, simply periodic hypersurfaces which have infinitely many parallel hyperplanar ends. By opposition with the 2-dimensional case, they are not foliated by spheres. Résumé. No...

The geometric maximum principle for smooth (spacelike) hypersurfaces, which is a consequence of Alexandrov’s [1] strong maximum for second order quasilinear elliptic operators, is a basic tool in Riemannian and Lorentzian geometry. In [2], extending earlier work of Eschenburg [7], a version of the geometric maximum principle in the Lorentzian setting was obtained for rough (C) spacelike hypersu...

The Chern-Moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries. Extending the work of N. K. Stanton, we consider the local equivalence problem for symmetric Levi degenerate hypersurfaces of finite type in C. The results give for all such hypersurfaces a complete normalization which respects the symmetries. In particular, they apply to tubes and rigi...