On some discrete inequalities in two independent variables
In this paper we establish some new nonlinear difference inequalities. We also present an application of one inequality to certain nonlinear sum-difference equation.
Real hypersurfaces in a nonflat complex space form and their almost contact metric structures
We characterize homogeneous real hypersurfaces of types (A₀), (A₁) and (B) in a complex projective space or a complex hyperbolic space.
Rotation surfaces with L₁-pointwise 1-type Gauss map in pseudo-Galilean 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.
Geometric properties of Lie hypersurfaces in a complex hyperbolic space
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.
A maximal inequality of non-negative submartingale.
Explicit bounds on some nonlinear integral inequalities.
An improvement of some inequalities similar to Hilbert's inequality.
Circular cone and its Gauss map
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...
On certain new integral inequalities and their applications.
Totally real submanifolds of a complex space form.
Hilbert-Pachpatte type integral inequalities and their improvement.
Some integral inequalities for functions of two variables.
New integral inequalities for iterated integrals with applications.
New retarded integral inequalities with applications.
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