Abstract : We establish a sharp integral inequality related to compact (without boundary) linear Weingarten hypersurfaces (immersed) in a locally symmetric Einstein manifold and we apply it to characterize totally umbilical hypersurfaces and isoparametric hypersurfaces with two distinct principal curvatures, one which is simple, in such an ambient space. Our approach is based on the ideas and techniques introduced by Al\'{\i}as and Mel\'{e}ndez in [4] for the case of hypersurfaces with constant scalar curvature in an Euclidean round sphere.
Abstract : This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give an existence of unique range sets for meromorphic functions that are the zero sets of some polynomials that do not necessarily satisfy the Fujimoto's hypothesis ([6]).
Abstract : Let $R$ be a commutative ring with identity. We call the ring $R$ to be an almost quasi-coherent ring if for any finite set of elements $a_{1},\dots,a_{p}$ and $a$ of $R$, there exists a positive integer $m$ such that the ideals $\bigcap_{i=1}^p Ra_{i}^{m}$ and $Ann_{R}(a^{m})$ are finitely generated, and to be almost von Neumann regular rings if for any two elements $a$ and $b$ in $R$, there exists a positive integer $n$ such that the ideal $(a^{n}, b^{n})$ is generated by an idempotent element. This paper establishes necessary and sufficient conditions for the Nagata's idealization and the amalgamated algebra to inherit these notions. Our results allow us to construct original examples of rings satisfying the above-mentioned properties.
Abstract : In this paper, we derive a Reilly-type inequality for the Laplacian with density on weighted manifolds with boundary. As its applications, we obtain some new Poincar\'{e}-type inequalities not only on weighted manifolds, but more interestingly, also on their boundary. Furthermore, some mean-curvature type inequalities on the boundary are also given.
Abstract : This paper is devoted to establishing certain $L^p$ bounds for the generalized parametric Marcinkiewicz integral operators associated to surfaces generated by polynomial compound mappings with rough kernels given by $h\in\Delta_\gamma(\mathbb{R}_{+})$ and $\Omega\in W\mathcal{F}_\beta({\rm S}^{n-1})$ for some $\gamma,\,\beta\in(1,\infty]$. As applications, the corresponding results for the generalized parametric Marcinkiewicz integral operators related to the Littlewood-Paley $g_\lambda^{*}$ functions and area integrals are also presented.
Abstract : We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.
Abstract : Applying the Lyapunov--Schmidt reduction, we consider \linebreak spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift--Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.
Abstract : In this paper, we study the Finsler warped product metric which is dually flat or projectively flat. The local structures of these metrics are completely determined. Some examples are presented.
Abstract : In this paper, we will prove the second main theorem for holomorphic curves intersecting the moving hypersurfaces in subgeneral position with index on an angular domain. Our results are an extension of the previous second main theorems for holomorphic curves with moving targets on an angular domain.
Abstract : In this paper, we establish an evaluation formula to calculate the Wiener integral of polynomials in terms of natural dual pairings on abstract Wiener spaces $(H,B,\nu)$. To do this we first derive a translation theorem for the Wiener integral of functionals associated with operators in $\mathcal L(B)$, the Banach space of bounded linear operators from $B$ to itself. We then apply the translation theorem to establish an integration by parts formula for the Wiener integral of functionals combined with operators in $\mathcal L(B)$. We finally apply this parts formula to evaluate the Wiener integral of certain polynomials in terms of natural dual pairings.
Zhicheng Wang
Bull. Korean Math. Soc. 2023; 60(1): 23-32
https://doi.org/10.4134/BKMS.b210703
Pigong Han, Keke Lei, Chenggang Liu, Xuewen Wang
Bull. Korean Math. Soc. 2022; 59(6): 1439-1470
https://doi.org/10.4134/BKMS.b210800
Preeti Dharmarha, Sarita Kumari
Bull. Korean Math. Soc. 2023; 60(1): 123-135
https://doi.org/10.4134/BKMS.b210931
Guanghui Lu, Shuangping Tao
Bull. Korean Math. Soc. 2022; 59(6): 1471-1493
https://doi.org/10.4134/BKMS.b210839
Xiao-Min Li, Yi-Xuan Li
Bull. Korean Math. Soc. 2023; 60(6): 1651-1672
https://doi.org/10.4134/BKMS.b220813
Cheng Gong, Jun Lu, Sheng-Li Tan
Bull. Korean Math. Soc. 2023; 60(5): 1365-1374
https://doi.org/10.4134/BKMS.b220710
Zaili Yan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(6): 1607-1620
https://doi.org/10.4134/BKMS.b220758
Bhagwati Duggal, In Hyoun Kim
Bull. Korean Math. Soc. 2023; 60(6): 1555-1566
https://doi.org/10.4134/BKMS.b220747
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