### A maximal inequality of non-negative submartingale.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

In this paper we establish some new nonlinear difference inequalities. We also present an application of one inequality to certain nonlinear sum-difference equation.

We characterize homogeneous real hypersurfaces of types (A₀), (A₁) and (B) in a complex projective space or a complex hyperbolic space.

We study rotation surfaces in the three-dimensional pseudo-Galilean space G₃¹ such that the Gauss map G satisfies the condition L₁G = f(G + C) for a smooth function f and a constant vector C, where L₁ is the Cheng-Yau operator.

We study homogeneous real hypersurfaces having no focal submanifolds in a complex hyperbolic space. They are called Lie hypersurfaces in this space. We clarify the geometry of Lie hypersurfaces in terms of their sectional curvatures, the behavior of the characteristic vector field and their holomorphic distributions.

The family of cones is one of typical models of non-cylindrical ruled surfaces. Among them, the circular cones are unique in the sense that their Gauss map satisfies a partial differential equation similar, though not identical, to one characterizing the so-called 1-type submanifolds. Specifically, for the Gauss map G of a circular cone, one has ΔG = f(G+C), where Δ is the Laplacian operator, f is a non-zero function and C is a constant vector. We prove that circular cones are characterized by being...

**Page 1**