On an inequality of Brendle in the hyperbolic space

We give a spinorial proof of a Heintze–Karcher-type inequality in the hyperbolic space proved by Brendle [4]. The proof relies on a generalized Reilly formula on spinors recently obtained in [7].     

Separation properties of induced I(L)-topological spaces

The concept of induced I(L)-topological spaces has been introduced by Kubiak (Ph.D. Thesis, UAM, Poznan, 1985) and independently by Wang (Kexue Tongbao 34 (5) (1989) 333). In this paper, the separation properties in the sense of Hutton–Reilly of induced I(L)-topological spaces are investigated. The main result of the paper is a characterization of L-topological spaces by means of the appropriate Hutton–Reilly separation properties of its induced I(L)-topological space.     

On Presentations of Bruck–Reilly Extensions

We first consider the class of monoids in which every left invertible element is also right invertible, and prove that if a monoid belonging to this class admits a finitely presented Bruck–Reilly extension then it is finitely generated. This allow us to obtain necessary and sufficient conditions for the Bruck–Reilly extensions of this class of monoids to be finitely presented. We then prove that thes 𝒟-classes of a Bruck–Reilly extension of a Clifford monoid are Bruck–Reilly extensions of groups. This yields another necessary and sufficient condition for these Bruck–Reilly extensions to be finitely generated and presented. Finally, we show that a Bruck–Reilly extension of a Clifford monoid is finitely presented as an inverse monoid if and only if it is finitely presented as a monoid, and that this property cannot be generalized to Bruck–Reilly extensions of arbitrary inverse monoids.     

An existence theorem for generalized variational inequalities with discontinuous and pseudomonotone operators

This paper gives a solution existence theorem for a generalized variational inequality problem with an operator which is defined on an infinite dimensional space, which is C-pseudomonotone in the sense of Inoan and Kolumbán [D. Inoan, J. Kolumbán, On pseudomonotone set-valued mappings, Nonlinear Analysis 68 (2008) 47-53], but which may not be upper semicontinuous on finite dimensional subspaces. The proof of the theorem provides a new technique which reduces infinite variational inequality problems to finite ones. Two examples are given and analyzed to illustrate the theorem. Moreover, an example is presented to show that the C-pseudomonotonicity of the operator cannot be omitted in the theorem.     

Contact CR-Warped Product Submanifolds in Sasakian Space Forms

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. Afterwards, I. Hasegawa and the present author obtained a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. In this paper, we improve the above inequality for contact CR-warped products in Sasakian space forms. Some applications are derived. A classification of contact CR-warped products in spheres, which satisfy the equality case, identically, is given.Mathematics Subject Classifications (2000). 53C40, 53C25.     

A sequentially compact non-compact quasi-pseudometric space

We give an example of a sequentially compact non-compact quasipseudometric space, thus finding a negative answer to the problem posed byI. L. Reilly, P. V. Subrahmanyam andM. K. Vamanamurthy in [1].     

弱向量变分不等式解集的连通性

研究拓扑向量空间到连续线性映射空间映射的弱向量变分不等式和与之相关 的纯量型变分不等式解集的关系, 引入弱和强一致连续概念,利用纯量型变分不等式 解集所表征的集值映射的特性给出弱向量变分不等式解集连通的一个充分条件。     

索伯列夫嵌入不等式的证明

We consider the problem about the space embedded by tile space and the embed-ding inequality. With the Holder inequality and interpolation inequality, we give the proof of the space embedding theorem and the space holder embedding theorem.     

The Uncertainty Principle for the Two-Sided Quaternion Fourier Transform

In this paper, we give an upper bound for the first eigenvalue of the p-Laplacian of Finsler submanifolds in Minkowski spaces. Our results extend those of Wu (Ann Glob Anal Geom 29:95–102, 2006), and Du and Mao (Front Math China 10:583–594, 2015).

     

Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians

In this Note, we extend the Reilly formula for drifting Laplacian operator and apply it to study eigenvalue estimate for drifting Laplacian operators on compact Riemannian manifolds' boundary. Our results on eigenvalue estimates extend previous results of Reilly and Choi and Wang.