Higher-dimensional Scherk's hypersurfaces

Higher dimensional Scherk’s hypersurfaces

In 3-dimensional Euclidean space Scherk second surfaces are singly periodic embedded minimal surfaces with 4 planar ends. In this paper, we obtain a natural generalization of Scherk’s second surfaces in higher dimensional Euclidean spaces. In particular we show that, in higher dimensional Euclidean spaces R, for n ≥ 3, there exists n−1-periodic embedded minimal hypersurfaces with 4 hyperplanar ...

Four-Dimensional Projective Orbifold Hypersurfaces

We classify four-dimensional quasismooth weighted hypersurfaces with small canonical class, and verify a conjecture of Johnson and Kollár on infinite series of quasismooth hypersurfaces with anticanonical hyperplane section in the case of fourfolds. By considering the quotient singularities that arise, we classify those weighted hypersurfaces that are canonical, Calabi–Yau, and Fano fourfolds. ...

Higher Order Invariants of Levi Degenerate Hypersurfaces

The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and analogous results for finite groups. The second part considers hypersurfaces of finite Catlin multitype, and the Kohn-Nirenberg phenomenon in higher dimensions...

Biharmonic Hypersurfaces in 4-dimensional Space Forms

We investigate proper biharmonic hypersurfaces with at most three distinct principal curvatures in space forms. We obtain the full classification of proper biharmonic hypersurfaces in 4-dimensional space forms.

Higher Dimensional