共查询到20条相似文献,搜索用时 343 毫秒
1.
Sharief Deshmukh 《Monatshefte für Mathematik》2012,166(1):93-106
In this paper, we show that an n-dimensional connected non-compact Ricci soliton isometrically immersed in the flat complex space form ${(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle )}$ , with potential vector field of the Ricci soliton is the characteristic vector field of the real hypersurface is an Einstein manifold. We classify connected Hopf hypersurfaces in the flat complex space form ${(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle )}$ and also obtain a characterization for the Hopf hypersurfaces in ${(C^{\frac{n+1}{2}},J,\left\langle ,\right\rangle ) }$ . 相似文献
2.
He-Jun Sun 《Archiv der Mathematik》2018,110(3):291-303
Let \(\Omega \) be a bounded domain with smooth boundary in an n-dimensional metric measure space \((\mathbb {R}^n, \langle ,\rangle , e^{-\phi }dv)\) and let \(\mathbf {u}=(u^1, \ldots , u^n)\) be a vector-valued function from \(\Omega \) to \(\mathbb {R}^n\). In this paper, we investigate the Dirichlet eigenvalue problem of a system of equations of the drifting Laplacian: \(\mathbb {L}_{\phi } \mathbf {u} + \alpha [ \nabla (\mathrm {div}\mathbf { u}) -\nabla \phi \mathrm {div} \mathbf {u}]= - \widetilde{\sigma } \mathbf {u}\), in \( \Omega \), and \(u|_{\partial \Omega }=0,\) where \(\mathbb {L}_{\phi } = \Delta - \nabla \phi \cdot \nabla \) is the drifting Laplacian and \(\alpha \) is a nonnegative constant. We establish some universal inequalities for lower order eigenvalues of this problem on the metric measure space \((\mathbb {R}^n, \langle ,\rangle , e^{-\phi }dv)\) and the Gaussian shrinking soliton \((\mathbb {R}^n, \langle ,\rangle _{\mathrm {can}}, e^{-\frac{|x|^2}{4}}dv, \frac{1}{2})\). Moreover, we give an estimate for the upper bound of the second eigenvalue of this problem in terms of its first eigenvalue on the gradient product Ricci soliton \((\Sigma \times \mathbb {R}, \langle ,\rangle , e^{-\frac{\kappa t^2}{2}}dv, \kappa )\), where \( \Sigma \) is an Einstein manifold with constant Ricci curvature \(\kappa \). 相似文献
3.
M. S. Sarsak 《Acta Mathematica Hungarica》2011,132(3):244-252
We introduce and study new separation axioms in generalized topological spaces, namely,
m-T\frac14\mu\mbox{-}T_{\frac{1}{4}},
m-T\frac38\mu \mbox{-}T_{\frac{3}{8}} and
m-T\frac12\mu\mbox{-}T_{\frac{1}{2}}.
m-T\frac14\mu\mbox{-}T_{\frac{1}{4}} spaces are strictly placed between μ-T
0 spaces and
m-T\frac38\mu\mbox{-}T_{\frac{3}{8}},
m-T\frac38\mu\mbox{-}T_{\frac{3}{8}} spaces are strictly placed between
m-T\frac14\mu\mbox{-}T_{\frac{1}{4}} spaces and
m-T\frac12\mu \mbox{-}T_{\frac{1}{2}} spaces, and
m-T\frac12\mu\mbox{-}T_{\frac{1}{2}} spaces are strictly placed between
m-T\frac38\mu\mbox{-}T_{\frac{3}{8}} spaces and μ-T
1 spaces. 相似文献
4.
The class of finitely presented groups
is an extension of the class of triangle groups studied recently. These groups are finite and their orders depend on the Lucas
numbers. In this paper, by considering the three presentations
and
we study Mon(π
i
), i=1,2,3, and Sg(π
i
), i=2,3, for their finiteness. In this investigation, we find their relationship with Gp(π
i
), where Mon(π), Sg(π) and Gp(π) are used for the monoid, the semigroup and the group presented by the presentation π, respectively. 相似文献
5.
We study the Γ-convergence of the following functional (p > 2)
$F_{\varepsilon}(u):=\varepsilon^{p-2}\int\limits_{\Omega}
|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\varepsilon^{\frac{p-2}{p-1}}}
\int\limits_{\Omega}
W(u) d(x,\partial \Omega)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrt{\varepsilon}}
\int\limits_{\partial\Omega}
V(Tu)d\mathcal{H}^2,$F_{\varepsilon}(u):=\varepsilon^{p-2}\int\limits_{\Omega}
|Du|^p d(x,\partial \Omega)^{a}dx+\frac{1}{\varepsilon^{\frac{p-2}{p-1}}}
\int\limits_{\Omega}
W(u) d(x,\partial \Omega)^{-\frac{a}{p-1}}dx+\frac{1}{\sqrt{\varepsilon}}
\int\limits_{\partial\Omega}
V(Tu)d\mathcal{H}^2, 相似文献
6.
Tuoc Van Phan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,4(1):395-400
Let Ω be an open, bounded domain in
\mathbbRn (n ? \mathbbN){\mathbb{R}^n\;(n \in \mathbb{N})} with smooth boundary ∂Ω. Let p, q, r, d
1, τ be positive real numbers and s be a non-negative number which satisfies
0 < \fracp-1r < \fracqs+1{0 < \frac{p-1}{r} < \frac{q}{s+1}}. We consider the shadow system of the well-known Gierer–Meinhardt system:
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