共查询到20条相似文献,搜索用时 31 毫秒
1.
Juan A. Aledo Victorino Lozano José A. Pastor 《Mediterranean Journal of Mathematics》2010,7(3):263-270
We prove that the only compact surfaces of positive constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} (resp. positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}}) whose boundary Γ is contained in a slice of the ambient space and such that the surface intersects this slice at a constant
angle along Γ, are the pieces of a rotational complete surface. We also obtain some area estimates for surfaces of positive
constant Gaussian curvature in
\mathbbH2×\mathbbR{\mathbb{H}^{2}\times\mathbb{R}} and positive constant Gaussian curvature greater than 1 in
\mathbbS2×\mathbbR{\mathbb{S}^{2}\times\mathbb{R}} whose boundary is contained in a slice of the ambient space. These estimates are optimal in the sense that if the bounds
are attained, the surface is again a piece of a rotational complete surface. 相似文献
2.
The field of quaternions, denoted by
\mathbbH{\mathbb{H}} can be represented as an isomorphic four dimensional subspace of
\mathbbR4×4{\mathbb{R}^{4\times 4}}, the space of real matrices with four rows and columns. In addition to the quaternions there is another four dimensional
subspace in
\mathbbR4×4{\mathbb{R}^{4\times 4}} which is also a field and which has – in connection with the quaternions – many pleasant properties. This field is called
field of pseudoquaternions. It exists in
\mathbbR4×4{\mathbb{R}^{4\times 4}} but not in
\mathbbH{\mathbb{H}}. It allows to write the quaternionic linear term axb in matrix form as Mx where x is the same as the quaternion x only written as a column vector in
\mathbbR4{\mathbb{R}^4}. And M is the product of the matrix associated with the quaternion a with the matrix associated with the pseudoquaternion b. 相似文献
3.
Jae-Young Chung 《Aequationes Mathematicae》2012,83(3):313-320
Let \mathbb R{\mathbb R} be the set of real numbers, f : \mathbb R ? \mathbb R{f : \mathbb {R} \to \mathbb {R}}, e 3 0{\epsilon \ge 0} and d > 0. We denote by {(x 1, y 1), (x 2, y 2), (x 3, y 3), . . .} a countable dense subset of \mathbb R2{\mathbb {R}^2} and let
$U_d:=\bigcup\nolimits_{j=1}^{\infty} \{(x, y)\in \mathbb {R}^2:\,|x|+|y| > d,\, |x-x_j| < 1,\, |y-y_j| < 2^{-j}\}.$U_d:=\bigcup\nolimits_{j=1}^{\infty} \{(x, y)\in \mathbb {R}^2:\,|x|+|y| > d,\, |x-x_j| < 1,\, |y-y_j| < 2^{-j}\}. 相似文献
4.
Suppose that Ω is a bounded domain with fractal boundary Γ in ${\mathbb R^{n+1}}
5.
Tobias Weth 《Archiv der Mathematik》2011,97(4):365-372
We consider the principal Dirichlet eigenfunction u of the Laplacian in a bounded region in
\mathbbR2{\mathbb{R}^2} which is convex in one direction, say in x
1. It has been asked by Kawohl (Remarks on some old and current eigenvalue problems, Cambridge University Press, pp 165–183,
1994) whether in this case u is quasiconcave in x
1, i.e., all superlevel sets of u are convex in x
1. In this note we provide a negative answer to this question by giving an explicit counterexample. 相似文献
6.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}
7.
The secant map of an immersion sends a pair of points to the direction of the line joining the images of the points under the immersion. The germ of the secant map of a generic codimension-c immersion $X\!\!:{\mathbb R}^n \to {\mathbb R}^{n+c}
8.
Let
H2\mathbb F{{\bf H}^{\bf 2}_{\mathbb F}} denote the two dimensional hyperbolic space over
\mathbb F{\mathbb F} , where
\mathbb F{\mathbb F} is either the complex numbers
\mathbb C{\mathbb C} or the quaternions
\mathbb H{\mathbb H} . It is of interest to characterize algebraically the dynamical types of isometries of
H2\mathbb F{{\bf H}^{\bf 2}_{\mathbb F}} . For
\mathbb F=\mathbb C{\mathbb F=\mathbb C} , such a characterization is known from the work of Giraud–Goldman. In this paper, we offer an algebraic characterization
of isometries of
H2\mathbb H{{\bf H}^{\bf 2}_{\mathbb H}} . Our result restricts to the case
\mathbb F=\mathbb C{\mathbb F=\mathbb C} and provides another characterization of the isometries of
H2\mathbb C{{\bf H}^{\bf 2}_{\mathbb C}} , which is different from the characterization due to Giraud–Goldman. Two elements in a group G are said to be in the same z-class if their centralizers are conjugate in G. The z-classes provide a finite partition of the isometry group. In this paper, we describe the centralizers of isometries of
H2\mathbb F{{\bf H}^{\bf 2}_{\mathbb F}} and determine the z-classes. 相似文献
9.
In this paper, we prove a suitable Trudinger–Moser inequality with a singular weight in
\mathbbRN{\mathbb{R}^N} and as an application of this result, using the mountain-pass theorem we establish sufficient conditions for the existence
of nontrivial solutions to quasilinear elliptic partial differential equations of the form
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |